910:(i.e., the incremental change in voltage due to an incremental change in temperature). Topological insulators are often composed of heavy atoms, which tends to lower thermal conductivity and are therefore beneficial for thermoelectrics. A recent study also showed that good electrical characteristics (i.e., electrical conductivity and Seebeck coefficient) can arise in topological insulators due to band inversion-driven warping of the bulk band structure. Often, the electrical conductivity and Seebeck coefficient are conflicting properties of thermoelectrics and difficult to optimize simultaneously. Band warping, induced by band inversion in a topological insulator, can mediate the two properties by reducing the effective mass of electrons/holes and increasing the valley degeneracy (i.e., the number of electronic bands that are contributing to charge transport). As a result, topological insulators are generally interesting candidates for thermoelectric applications.
575:) Hamiltonian that is topologically nontrivial. This system replicates the effective Hamiltonians from all universal classes of 1- to 3-D topological insulators. Interestingly, topological properties of Floquet topological insulators could be controlled via an external periodic drive rather than an external magnetic field. An atomic lattice empowered by distance selective Rydberg interaction could simulate different classes of FTI over a couple of hundred sites and steps in 1, 2 or 3 dimensions. The long-range interaction allows designing topologically ordered periodic boundary conditions, further enriching the realizable topological phases.
77:
942:(MBE). MBE has so far been the most common experimental technique. The growth of thin film topological insulators is governed by weak van der Waals interactions. The weak interaction allows to exfoliate the thin film from bulk crystal with a clean and perfect surface. The van der Waals interactions in epitaxy also known as van der Waals epitaxy (VDWE), is a phenomenon governed by weak van der Waal's interactions between layered materials of different or same elements in which the materials are stacked on top of each other. This approach allows the growth of layered topological insulators on other substrates for
1812:. These crystal structures can consist of a large number of elements. Band structures and energy gaps are very sensitive to the valence configuration; because of the increased likelihood of intersite exchange and disorder, they are also very sensitive to specific crystalline configurations. A nontrivial band structure that exhibits band ordering analogous to that of the known 2D and 3D TI materials was predicted in a variety of 18-electron half-Heusler compounds using first-principles calculations. These materials have not yet shown any sign of intrinsic topological insulator behavior in actual experiments.
1117:). The resulted single crystals have a well-defined crystallographic orientation; their composition, thickness, size, and the surface density on the desired substrate can be controlled. The thickness control is particularly important for 3D TIs in which the trivial (bulky) electronic channels usually dominate the transport properties and mask the response of the topological (surface) modes. By reducing the thickness, one lowers the contribution of trivial bulk channels into the total conduction, thus forcing the topological modes to carry the electric current.
115:
7303:
935:
990:
influence the growth rate and the ratio of species of source materials present at the substrate interface. Furthermore, in MBE, samples can be grown layer by layer which results in flat surfaces with smooth interface for engineered heterostructures. Moreover, MBE synthesis technique benefits from the ease of moving a topological insulator sample from the growth chamber to a characterization chamber such as angle-resolved photoemission spectroscopy (ARPES) or
7731:
7755:
25:
7767:
7743:
6828:
1767:. Different materials will have different wave propagation properties, and thus different vector bundles. If we consider all insulators (materials with a band gap), this creates a space of vector bundles. It is the topology of this space (modulo trivial bands) from which the "topology" in topological insulators arises.
1367:
on different substrates and the resulting lattice mismatch. Generally, regardless of the substrate used, the resulting films have a textured surface that is characterized by pyramidal single-crystal domains with quintuple-layer steps. The size and relative proportion of these pyramidal domains vary
989:
at the interface, the substrate and thin film are expected to have similar lattice constants. MBE has an advantage over other methods due to the fact that the synthesis is performed in high vacuum hence resulting in less contamination. Additionally, lattice defect is reduced due to the ability to
1368:
with factors that include film thickness, lattice mismatch with the substrate and interfacial chemistry-dependent film nucleation. The synthesis of thin films have the stoichiometry problem due to the high vapor pressures of the elements. Thus, binary tetradymites are extrinsically doped as n-type (
1782:
symmetries are usually significant in quantum mechanics, they have no effect on the topology here. Instead, the three symmetries typically considered are time-reversal symmetry, particle-hole symmetry, and chiral symmetry (also called sublattice symmetry). Mathematically, these are represented as,
570:
Topological insulators are challenging to synthesize, and limited in topological phases accessible with solid-state materials. This has motivated the search for topological phases on the systems that simulate the same principles underlying topological insulators. Discrete time quantum walks (DTQW)
1774:
of the space indicates how many different "islands" of insulators exist amongst the metallic states. Insulators in the connected component containing the vacuum state are identified as "trivial", and all other insulators as "topological". The connected component in which an insulator lies can be
372:
topological invariant was constructed and the importance of the time reversal symmetry was clarified in the work by Kane and Mele. Subsequently, Bernevig, Taylor L. Hughes and Zhang made a theoretical prediction that 2D topological insulator with one-dimensional (1D) helical edge states would be
1709:
The first step of topological insulators identification takes place right after synthesis, meaning without breaking the vacuum and moving the sample to an atmosphere. That could be done by using angle-resolved photoemission spectroscopy (ARPES) or scanning tunneling microscopy (STM) techniques.
1074:
The physical vapor deposition (PVD) technique does not suffer from the disadvantages of the exfoliation method and, at the same time, it is much simpler and cheaper than the fully controlled growth by molecular-beam epitaxy. The PVD method enables a reproducible synthesis of single crystals of
5950:
Tu, Ngoc Han, Tanabe, Yoichi; Satake, Yosuke, Huynh, Khuong Kim; Le, Phuoc Huu, Matsushita, Stephane Yu; Tanigaki, Katsumi (2017). "Large-Area and
Transferred High-Quality Three-Dimensional Topological Insulator Bi2–x Sb x Te3–y Se y Ultrathin Film by Catalyst-Free Physical Vapor Deposition".
1267:. However, the use of sapphire as substrate has not been so encouraging due to a large mismatch of about 15%. The selection of appropriate substrate can improve the overall properties of TI. The use of buffer layer can reduce the lattice match hence improving the electrical properties of TI.
1807:
The field of topological insulators still needs to be developed. The best bismuth chalcogenide topological insulators have about 10 meV bandgap variation due to the charge. Further development should focus on the examination of both: the presence of high-symmetry electronic bands and simply
176:, local (symmetry-preserving) perturbations cannot damage this surface state. This is unique to topological insulators: while ordinary insulators can also support conductive surface states, only the surface states of topological insulators have this robustness property.
587:
if superconductivity is induced on the surface of 3D topological insulators via proximity effects. (Note that
Majorana zero-mode can also appear without topological insulators.) The non-trivialness of topological insulators is encoded in the existence of a gas of
596:: the gapless surface states of topological insulators are symmetry-protected (i.e., not topological), while the gapless surface states in quantum Hall effect are topological (i.e., robust against any local perturbations that can break all the symmetries). The
6446:
Bansal, Namrata; Kim, Yong Seung; Edrey, Eliav; Brahlek, Matthew; Horibe, Yoichi; Iida, Keiko; Tanimura, Makoto; Li, Guo-Hong; Feng, Tian; Lee, Hang-Dong; Gustafsson, Torgny; Andrei, Eva; Oh, Seongshik (2011-10-31). "Epitaxial growth of topological insulator
1215:
S. The choice of chalcogenides is related to the van der Waals relaxation of the lattice matching strength which restricts the number of materials and substrates. Bismuth chalcogenides have been studied extensively for TIs and their applications in
303:
The first models of 3D topological insulators were proposed by B. A. Volkov and O. A. Pankratov in 1985, and subsequently by
Pankratov, S. V. Pakhomov, and Volkov in 1987. Gapless 2D Dirac states were shown to exist at the band inversion contact in
1710:
Further measurements includes structural and chemical probes such as X-ray diffraction and energy-dispersive spectroscopy but depending on the sample quality, the lack of sensitivity could remain. Transport measurements cannot uniquely pinpoint the
5398:
Hsieh, D.; D. Hsieh; Y. Xia; L. Wray; D. Qian; A. Pal; J. H. Dil; F. Meier; J. Osterwalder; C. L. Kane; G. Bihlmayer; Y. S. Hor; R. J. Cava; M. Z. Hasan (2009). "Observation of
Unconventional Quantum Spin Textures in Topological Insulators".
4303:
Xu, Y; Miotkowski, I.; Liu, C.; Tian, J.; Nam, H.; Alidoust, N.; Hu, J.; Shih, C.-K; Hasan, M.Z.; Chen, Y.-P. (2014). "Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator".
489:
are now believed to exhibit topological surface states. In some of these materials, the Fermi level actually falls in either the conduction or valence bands due to naturally-occurring defects, and must be pushed into the bulk gap by
376:
Although the topological classification and the importance of time-reversal symmetry was pointed in the 2000s, all the necessary ingredients and physics of topological insulators were already understood in the works from the 1980s.
80:
An (informal) phase diagram with topological insulators, trivial insulators, and conductors. There is no path from the topological insulators to the trivial insulators that does not cross the conducting phase. The diagram depicts a
5599:
Chang, Cui-Zu; Zhang, Jinsong; Feng, Xiao; Shen, Jie; Zhang, Zuocheng; Guo, Minghua; Li, Kang; Ou, Yunbo; Wei, Pang (2013-04-12). "Experimental
Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator".
4078:
Lin, Hsin; L. Andrew Wray; Yuqi Xia; Suyang Xu; Shuang Jia; Robert J. Cava; Arun Bansil; M. Zahid Hasan (July 2010). "Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena".
7048:
Hasan, M. Zahid; Xu, Su-Yang; Neupane, M (2015). "Topological
Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators". In Ortmann, F.; Roche, S.; Valenzuela, S. O. (eds.).
373:
realized in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride. The transport due to 1D helical edge states was indeed observed in the experiments by
Molenkamp's group in 2007.
4829:
Mellnik, A. R; Lee, J. S; Richardella, A; Grab, J. L; Mintun, P. J; Fischer, M. H; Vaezi, A; Manchon, A; Kim, E. -A; Samarth, N; Ralph, D. C (2014). "Spin-transfer torque generated by a topological insulator".
592:. Dirac particles which behave like massless relativistic fermions have been observed in 3D topological insulators. Note that the gapless surface states of topological insulators differ from those in the
513:
S) with slightly Sn - doping, exhibits an intrinsic semiconductor behavior with Fermi energy and Dirac point lie in the bulk gap and the surface states were probed by the charge transport experiments.
4017:
Chadov, Stanislav; Xiao-Liang Qi; Jürgen Kübler; Gerhard H. Fecher; Claudia Felser; Shou-Cheng Zhang (July 2010). "Tunable multifunctional topological insulators in ternary
Heusler compounds".
6154:
Jerng, Sahng-Kyoon; Joo, Kisu; Kim, Youngwook; Yoon, Sang-Moon; Lee, Jae Hong; Kim, Miyoung; Kim, Jun Sung; Yoon, Euijoon; Chun, Seung-Hyun (2013). "Ordered growth of topological insulator
4229:
Noh, H.-J.; H. Koh; S.-J. Oh; J.-H. Park; H.-D. Kim; J. D. Rameau; T. Valla; T. E. Kidd; P. D. Johnson; Y. Hu; Q. Li (2008). "Spin-orbit interaction effect in the electronic structure of
183:
transformed into an ordinary insulator without passing through an intermediate conducting state. In other words, topological insulators and trivial insulators are separate regions in the
6905:
Zhang, X.M.; Liu, E.K.; Liu, Z.Y.; Liu, G.D.; Wu, G.H.; Wang, W.H. (2013-04-01). "Prediction of topological insulating behavior in inverse
Heusler compounds from first principles".
3817:
Hasan, M. Zahid; Xu, Su-Yang; Neupane, Madhab (2015), "Topological
Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators",
501:
Fully bulk-insulating or intrinsic 3D topological insulator states exist in Bi-based materials as demonstrated in surface transport measurements. In a new Bi based chalcogenide (Bi
6529:
Zhang, Guanhua; Qin, Huajun; Teng, Jing; Guo, Jiandong; Guo, Qinlin; Dai, Xi; Fang, Zhong; Wu, Kehui (2009-08-03). "Quintuple-layer epitaxy of thin films of topological insulator
1795:
with the Hamiltonian; and a unitary operator which anti-commutes with the Hamiltonian. All combinations of the three together with each spatial dimension result in the so-called
161:
transformed into a trivial one without untwisting the bands, which closes the band gap and creates a conducting state. Thus, due to the continuity of the underlying field, the
3921:
Chiatti, Olivio; Riha, Christian; Lawrenz, Dominic; Busch, Marco; Dusari, Srujana; Sánchez-Barriga, Jaime; Mogilatenko, Anna; Yashina, Lada V.; Valencia, Sergio (2016-06-07).
1737:
837:
775:
740:
710:
681:
652:
623:
370:
245:
108:
4140:
Hsieh, D.; Y. Xia; D. Qian; L. Wray; F. Meier; J. H. Dil; J. Osterwalder; L. Patthey; A. V. Fedorov; H. Lin; A. Bansil; D. Grauer; Y. S. Hor; R. J. Cava; M. Z. Hasan (2009).
788:
labelled by the type of discrete symmetry (time-reversal symmetry, particle-hole symmetry, and chiral symmetry) has a corresponding group of topological invariants (either
808:
267:
906:(p-type thermoelectrics). High thermoelectric power conversion efficiency is realized in materials with low thermal conductivity, high electrical conductivity, and high
157:
of the material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator. The topological insulator cannot be
272:
The surface states of topological insulators can have exotic properties. For example, in time-reversal symmetric 3D topological insulators, surface states have their
7217:
6111:
Cui, Hongmei; Liu, Hong; Wang, Jiyang; Li, Xia; Han, Feng; Boughton, R.I. (2004-11-15). "Sonochemical synthesis of bismuth selenide nanobelts at room temperature".
5860:
Alegria, L. D.; Schroer, M. D.; Chatterjee, A.; Poirier, G. R.; Pretko, M.; Patel, S. K.; Petta, J. R. (2012-08-06). "Structural and Electrical Characterization of
516:
It was proposed in 2008 and 2009 that topological insulators are best understood not as surface conductors per se, but as bulk 3D magnetoelectrics with a quantized
2998:
Roy, Rahul (2009-05-21). "Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect".
520:
effect. This can be revealed by placing topological insulators in magnetic field. The effect can be described in language similar to that of the hypothetical
2657:
König, Markus; Wiedmann, Steffen; Brüne, Christoph; Roth, Andreas; Buhmann, Hartmut; Molenkamp, Laurens W.; Qi, Xiao-Liang; Zhang, Shou-Cheng (2007-11-02).
4492:
Essin, Andrew M.; Moore, Joel E.; Vanderbilt, David (2009-04-10). "Magnetoelectric Polarizability and Axion Electrodynamics in Crystalline Insulators".
625:
topological invariants cannot be measured using traditional transport methods, such as spin Hall conductance, and the transport is not quantized by the
276:
locked at a right-angle to their momentum (spin-momentum locking). At a given energy the only other available electronic states have different spin, so
997:
Due to the weak van der Waals bonding, which relaxes the lattice-matching condition, TI can be grown on a wide variety of substrates such as Si(111),
42:
1246:
Bismuth chalcogenides have been successfully grown on different substrates. In particular, Si has been a good substrate for the successful growth of
6012:
7011:
5791:
Witting, Ian T.; Chasapis, Thomas C.; Ricci, Francesco; Peters, Matthew; Heinz, Nicholas A.; Hautier, Geoffroy; Snyder, G. Jeffrey (June 2019).
3219:
3157:
Shuichi Murakami (2007). "Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase".
198:
The properties of topological insulators and their surface states are highly dependent on both the dimension of the material and its underlying
38:
6603:
Richardella, A.; Zhang, D. M.; Lee, J. S.; Koser, A.; Rench, D. W.; Yeats, A. L.; Buckley, B. B.; Awschalom, D. D.; Samarth, N. (2010-12-27).
7210:
283:
Despite their origin in quantum mechanical systems, analogues of topological insulators can also be found in classical media. There exist
3744:
Hsieh, D.; Xia, Y.; Wray, L.; Qian, D.; Pal, A.; Dil, J. H.; Osterwalder, J.; Meier, F.; Bihlmayer, G.; Kane, C. L.; et al. (2009).
1431:). Due to the weak van der Waals bonding, graphene is one of the preferred substrates for TI growth despite the large lattice mismatch.
5337:
Potter, Andrew C.; Lee, Patrick A. (23 March 2012). "Topological superconductivity and Majorana fermions in metallic surface states".
7747:
4431:
Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng (2008-11-24). "Topological field theory of time-reversal invariant insulators".
478:
423:
6361:
327:
Later sets of theoretical models for the 2D topological insulator (also known as the quantum spin Hall insulators) were proposed by
7203:
3540:
Behnia, Kamran; Balicas, Luis; Kopelevich, Yakov (2007-09-21). "Signatures of Electron Fractionalization in Ultraquantum Bismuth".
2383:
Khanikaev, Alexander B.; Hossein Mousavi, S.; Tse, Wang-Kong; Kargarian, Mehdi; MacDonald, Allan H.; Shvets, Gennady (March 2013).
1851:
1796:
1748:
840:
206:. Some combinations of dimension and symmetries forbid topological insulators completely. All topological insulators have at least
203:
571:
have been proposed for making Floquet topological insulators (FTI). This periodically driven system simulates an effective (
6313:
Heremans, Joseph P.; Cava, Robert J.; Samarth, Nitin (2017-09-05). "Tetradymites as thermoelectrics and topological insulators".
1756:
allows a full characterization of the wave propagation properties of a material by assigning a matrix to each wave vector in the
919:
7184:
6026:
Wang, Debao; Yu, Dabin; Mo, Maosong; Liu, Xianming; Qian, Yitai (2003-06-01). "Preparation and characterization of wire-like
3834:
1220:. The van der Waals interaction in TIs exhibit important features due to low surface energy. For instance, the surface of
215:
962:
method for the growth of a crystalline material on a crystalline substrate to form an ordered layer. MBE is performed in
2511:
He, Cheng; Ni, Xu; Ge, Hao; Sun, Xiao-Chen; Chen, Yan-Bin; Lu, Ming-Hui; Liu, Xiao-Ping; Chen, Yan-Feng (December 2016).
7793:
7735:
7066:
61:
1831:
7112:
4805:
3444:
Buot, F. A. (1973-09-01). "Weyl Transform and the Magnetic Susceptibility of a Relativistic Dirac Electron Gas".
1788:
288:
35:
5831:
126:
falls within the bulk band gap which is traversed by topologically-protected spin-textured Dirac surface states.
1861:
1771:
981:
MBE is an appropriate technique for the growth of high quality single-crystal films. In order to avoid a huge
971:
555:
455:
284:
5546:
Chiu, C.; J. Teo; A. Schnyder; S. Ryu (2016). "Classification of topological quantum matter with symmetries".
49:
7771:
7716:
7327:
2319:
991:
859:
199:
5215:"Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction"
7262:
1826:
495:
384:, and in particular "strong topological insulators" exist that cannot be reduced to multiple copies of the
154:
6683:
Kong, D.; Dang, W.; Cha, J.J.; Li, H.; Meister, S.; Peng, H. K.; Cui, Y (2010). "SFew-layer nanoplates of
6391:"Review of 3D topological insulator thin-film growth by molecular beam epitaxy and potential applications"
1778:
This space can be restricted under the presence of symmetries, changing the resulting topology. Although
269:, allow classification of insulators as trivial or topological, and can be computed by various methods.
7507:
7416:
1836:
1713:
813:
751:
716:
686:
657:
628:
599:
380:
In 2007, it was predicted that 3D topological insulators might be found in binary compounds involving
346:
221:
84:
7456:
7431:
6963:
925:
846:
The most promising applications of topological insulators are spintronic devices and dissipationless
173:
119:
2607:"Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1-xSnxTe and Hg1-xCdxTe"
982:
583:
Spin-momentum locking in the topological insulator allows symmetry-protected surface states to host
7626:
7380:
7370:
7226:
1846:
1792:
1217:
879:
855:
525:
385:
320:
heterostructures. Existence of interface Dirac states in HgTe/CdTe was experimentally verified by
187:, connected only by conducting phases. In this way, topological insulators provide an example of a
146:
5274:"Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator"
862:. In addition, topological insulator materials have also found practical applications in advanced
791:
250:
76:
7798:
7472:
6788:"Josephson current mediated by ballistic topological states in Bi2Te2.3Se0.7 single nanocrystals"
5080:"Toward simulation of topological phenomena with one-, two-, and three-dimensional quantum walks"
1998:
986:
139:
179:
This leads to a more formal definition of a topological insulator: an insulator which cannot be
7117:
929:
559:
211:
135:
5671:"Intrinsically core-shell plasmonic dielectric nanostructures with ultrahigh refractive index"
5460:
Read, N.; Sachdev, Subir (1991). "Large-N expansion for frustrated quantum antiferromagnets".
4141:
7523:
7436:
6006:
5792:
4673:"Hopes surface for exotic insulator: Findings by three teams may solve a 40-year-old mystery"
4614:"Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator"
3349:
3043:
Liang Fu; C. L. Kane; E. J. Mele (2007-03-07). "Topological insulators in three dimensions".
2353:
1970:
589:
214:
from the absence of a magnetic field. In this way, topological insulators are an example of
7492:
7267:
7028:
6982:
6799:
6744:
6647:
6569:
6487:
6402:
6322:
6194:
6120:
6077:
5970:
5900:
5747:
5682:
5619:
5565:
5512:
5469:
5418:
5356:
5295:
5236:
5166:
5101:
5044:
4979:
4914:
4849:
4755:
4684:
4635:
4570:
4511:
4450:
4323:
4269:
4195:
4098:
4036:
3965:
3869:
3767:
3694:
3632:
3559:
3498:
3453:
3402:
3337:
3281:
3236:
3176:
3123:
3062:
2948:
2883:
2818:
2753:
2680:
2618:
2534:
2469:
2406:
2341:
2276:
2210:
2142:
2072:
2017:
1958:
1889:
1784:
974:. The gaseous elements then condense on the wafer where they react with each other to form
551:
321:
5503:
Wen, Xiao-Gang (1991). "Mean Field Theory of Spin Liquid States with Finite Energy Gaps".
4142:"Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in
8:
7446:
7426:
7411:
7360:
6881:
2861:
2796:
2731:
1841:
1036:
907:
784:) for each spatial dimensionality, each of the ten Altland—Zirnbauer symmetry classes of
593:
544:
273:
158:
7032:
6986:
6803:
6748:
6651:
6573:
6491:
6406:
6326:
6198:
6124:
6081:
5974:
5949:
5904:
5751:
5686:
5623:
5569:
5516:
5473:
5422:
5360:
5299:
5240:
5170:
5105:
5048:
4983:
4918:
4853:
4759:
4688:
4639:
4574:
4515:
4454:
4327:
4273:
4199:
4102:
4040:
3969:
3873:
3771:
3698:
3636:
3563:
3502:
3457:
3406:
3341:
3285:
3240:
3180:
3127:
3066:
2952:
2887:
2822:
2757:
2684:
2622:
2538:
2473:
2410:
2345:
2280:
2214:
2146:
2076:
2021:
1962:
1893:
1075:
various layered quasi-two-dimensional materials including topological insulators (i.e.,
7593:
7583:
7421:
7332:
7167:
7140:
6998:
6972:
6940:
6914:
6817:
6768:
6734:
6637:
6559:
6511:
6477:
6428:
6290:
6256:
6226:
6184:
5994:
5960:
5932:
5890:
5768:
5735:
5711:
5670:
5651:
5609:
5581:
5555:
5442:
5408:
5380:
5346:
5319:
5285:
5254:
5226:
5214:
5190:
5156:
5125:
5091:
5060:
5034:
5003:
4969:
4938:
4904:
4873:
4839:
4787:
4745:
4625:
4543:
4501:
4474:
4440:
4408:
4385:
4361:
4339:
4313:
4285:
4259:
4088:
4060:
4026:
3994:
3955:
3922:
3903:
3799:
3757:
3726:
3684:
3648:
3622:
3591:
3549:
3522:
3488:
3426:
3392:
3361:
3327:
3297:
3271:
3262:
Fu, Liang; Kane, C. L. (2007-07-02). "Topological insulators with inversion symmetry".
3200:
3166:
3139:
3113:
3086:
3052:
3025:
3007:
2980:
2938:
2907:
2873:
2842:
2808:
2777:
2743:
2712:
2670:
2558:
2524:
2493:
2438:
2396:
2365:
2331:
2300:
2266:
2226:
2200:
2166:
2132:
2041:
2007:
1974:
1948:
1921:
1753:
1346:
1193:
1125:
Thus far, the field of topological insulators has been focused on bismuth and antimony
947:
863:
529:
474:
408:
336:
277:
114:
6089:
3745:
3104:
Fu, Liang; C. L. Kane (2007-07-02). "Topological insulators with inversion symmetry".
2926:
2658:
2606:
2254:
2188:
2120:
2061:"Band inversion mechanism in topological insulators: A guideline for materials design"
2060:
7754:
7701:
7666:
7573:
7497:
7172:
7099:
7062:
7040:
6932:
6821:
6760:
6665:
6585:
6515:
6503:
6420:
6338:
6294:
6282:
6274:
6218:
6210:
6136:
6093:
5998:
5986:
5924:
5916:
5812:
5773:
5716:
5698:
5643:
5635:
5585:
5528:
5485:
5446:
5434:
5372:
5311:
5258:
5182:
5129:
5117:
4995:
4930:
4877:
4865:
4791:
4779:
4771:
4710:
4702:
4653:
4594:
4586:
4535:
4527:
4478:
4466:
4413:
4211:
4122:
4114:
4052:
3999:
3981:
3895:
3887:
3830:
3803:
3791:
3783:
3718:
3710:
3583:
3575:
3514:
3418:
3353:
3248:
3192:
3078:
3029:
2972:
2964:
2899:
2834:
2769:
2704:
2696:
2634:
2630:
2562:
2550:
2485:
2430:
2422:
2357:
2292:
2170:
2158:
2098:
2033:
1913:
1905:
1821:
1222:
967:
745:
584:
533:
470:
401:
397:
317:
313:
180:
7002:
6944:
6928:
6772:
6432:
6230:
5936:
5655:
5384:
5194:
5064:
5007:
4942:
4343:
4064:
3907:
3652:
3595:
3365:
3318:
Hasan, M. Zahid; Moore, Joel E. (2011). "Three-Dimensional Topological Insulators".
3301:
3204:
3188:
3143:
2580:
2497:
2457:
2442:
2369:
2304:
2230:
1978:
491:
7671:
7563:
7543:
7538:
7533:
7528:
7385:
7365:
7322:
7287:
7257:
7162:
7152:
7127:
7089:
7054:
7036:
6990:
6924:
6861:
6807:
6786:
Stolyarov, V.S.; Yakovlev, D.S.; Kozlov, S.N.; Skryabina, O.V.; Lvov, D.S. (2020).
6752:
6655:
6577:
6495:
6410:
6330:
6266:
6202:
6132:
6128:
6085:
5978:
5908:
5837:
5804:
5763:
5755:
5706:
5690:
5627:
5573:
5520:
5477:
5426:
5364:
5323:
5307:
5303:
5244:
5174:
5109:
5052:
4987:
4922:
4857:
4767:
4763:
4692:
4643:
4578:
4547:
4523:
4519:
4458:
4403:
4395:
4331:
4289:
4281:
4277:
4207:
4203:
4106:
4044:
3989:
3973:
3877:
3822:
3775:
3730:
3702:
3640:
3567:
3526:
3506:
3461:
3430:
3410:
3345:
3289:
3244:
3184:
3131:
3090:
3070:
3017:
2984:
2956:
2911:
2891:
2846:
2826:
2781:
2761:
2716:
2688:
2626:
2542:
2477:
2414:
2349:
2284:
2218:
2150:
2088:
2080:
2045:
2025:
1966:
1925:
1897:
1856:
1809:
1302:
1027:
1021:
851:
536:
who showed that the Faraday rotation was quantized by the fine structure constant.
486:
482:
466:
3510:
3074:
2895:
2830:
2765:
2029:
7696:
7651:
7317:
7234:
5982:
5841:
5577:
5273:
5079:
4729:
4016:
3610:
2927:"Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells"
1031:
999:
517:
439:
340:
328:
188:
7141:"Topological insulators promise computing advances, insights into matter itself"
5481:
5144:
5113:
4582:
4359:
461:
Shortly thereafter symmetry-protected surface states were also observed in pure
7759:
7706:
7588:
7477:
6994:
6832:
6334:
5368:
5178:
4956:
Cayssol, Jérôme; Dóra, Balázs; Simon, Ferenc; Moessner, Roderich (2013-01-28).
4462:
3746:"Observation of Unconventional Quantum Spin Textures in Topological Insulators"
3644:
3479:
Kane, C. L.; Mele, E. J. (2005-11-23). "Quantum Spin Hall Effect in Graphene".
3380:
3293:
3135:
3021:
2222:
2154:
2084:
1779:
1757:
975:
943:
867:
572:
451:
435:
332:
305:
7058:
6812:
6787:
6499:
5249:
4612:
Wu, Liang; Salehi, M.; Koirala, N.; Moon, J.; Oh, S.; Armitage, N. P. (2016).
3826:
3672:
2481:
454:. This prediction is of particular interest due to the observation of charge
7787:
7631:
7613:
7598:
7578:
7482:
7451:
7282:
7019:
6936:
6669:
6589:
6507:
6424:
6342:
6278:
6214:
6140:
6097:
5920:
5816:
5702:
5639:
5524:
5376:
5186:
5121:
4999:
4934:
4775:
4733:
4706:
4590:
4531:
4470:
4118:
3985:
3891:
3787:
3714:
3579:
3357:
3227:
3196:
2968:
2700:
2638:
2554:
2489:
2426:
2361:
2296:
2162:
2102:
1939:
Hasan, M.Z.; Moore, J.E. (2011). "Three-Dimensional Topological Insulators".
1909:
1764:
785:
494:
or gating. The surface states of a 3D topological insulator is a new type of
309:
192:
184:
162:
48:
Please replace inadequate primary references with secondary sources. See the
7157:
5631:
5430:
5143:
Kitagawa, Takuya; Rudner, Mark S.; Berg, Erez; Demler, Eugene (2010-09-24).
4957:
4892:
4648:
4613:
3779:
3673:"A tunable topological insulator in the spin helical Dirac transport regime"
3571:
3465:
2960:
2692:
970:, the elements are heated in different electron beam evaporators until they
7568:
7390:
7292:
7195:
7176:
7103:
6764:
6415:
6390:
6286:
6222:
5990:
5928:
5808:
5777:
5734:
Yue, Zengji; Xue, Gaolei; Liu, Juan; Wang, Yongtian; Gu, Min (2017-05-18).
5720:
5694:
5647:
5489:
5438:
5315:
4991:
4926:
4869:
4783:
4714:
4657:
4598:
4539:
4417:
4215:
4126:
4056:
4003:
3899:
3882:
3857:
3795:
3722:
3587:
3518:
3422:
3379:
Hsieh, David; Dong Qian; Andrew L. Wray; Yuqi Xia; Yusan Hor; Robert Cava;
3082:
2976:
2903:
2838:
2773:
2708:
2512:
2434:
2384:
2037:
1917:
1126:
777:
540:
442:
points and the bulk features massive Dirac fermions. Additionally, bulk Bi
169:, which is topologically trivial) is forced to support a conducting state.
5669:
Yue, Zengji; Cai, Boyuan; Wang, Lan; Wang, Xiaolin; Gu, Min (2016-03-01).
5532:
4561:
Wilczek, Frank (1987-05-04). "Two applications of axion electrodynamics".
142:, meaning that electrons can only move along the surface of the material.
7688:
7406:
7375:
7355:
7302:
6866:
6849:
6247:
Geim, A. K.; Grigorieva, I. V. (2013). "Van der Waals heterostructures".
3493:
3276:
3118:
3057:
3012:
2943:
2878:
2813:
2748:
2012:
934:
713:
554:, can be manipulated by topological insulators. The effect is related to
280:
is strongly suppressed and conduction on the surface is highly metallic.
172:
Since this results from a global property of the topological insulator's
123:
6270:
5759:
4861:
4399:
3706:
3414:
2925:
Bernevig, B. Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng (2006-12-15).
2093:
1901:
7603:
7441:
7277:
6850:"Topological Insulator Film Growth by Molecular Beam Epitaxy: A Review"
6206:
5022:
3856:
Chen, Xi; Ma, Xu-Cun; He, Ke; Jia, Jin-Feng; Xue, Qi-Kun (2011-03-01).
847:
683:
topological invariants was demonstrated which provide a measure of the
6882:"10 symmetry classes and the periodic table of topological insulators"
6756:
6660:
6604:
6581:
5912:
5056:
4335:
3977:
3383:(2008). "A Topological Dirac insulator in a quantum spin Hall phase".
2546:
2456:
Tokura, Yoshinori; Yasuda, Kenji; Tsukazaki, Atsushi (February 2019).
2288:
7661:
7487:
7272:
4110:
4048:
2418:
419:
407:
The first 3D topological insulator to be realized experimentally was
292:
7094:
7077:
6961:
Hasan, M. Zahid; Kane, Charles L. (2010). "Topological Insulators".
4697:
4672:
3378:
2382:
1775:
identified with a number, referred to as a "topological invariant".
918:
Topological insulators can be grown using different methods such as
5965:
5614:
5560:
5231:
5096:
4630:
4390:
3960:
2529:
2513:"Acoustic topological insulator and robust one-way sound transport"
2059:
Zhu, Zhiyong; Cheng, Yingchun; Schwingenschlögl, Udo (2012-06-01).
498:(2DEG) where the electron's spin is locked to its linear momentum.
462:
396:
2D Topological insulators were first realized in system containing
150:
110:
topological invariant, since there are two "islands" of insulators.
6977:
6919:
6739:
6642:
6564:
6482:
6261:
6189:
5895:
5881:
Nanostructures Grown by Metal–Organic Chemical Vapor Deposition".
5413:
5351:
5290:
5161:
5039:
4974:
4909:
4844:
4750:
4506:
4445:
4318:
4302:
4264:
4093:
4077:
4031:
3762:
3689:
3627:
3554:
3397:
3332:
3171:
2675:
2401:
2336:
2271:
2205:
2137:
1953:
7711:
7678:
7656:
7636:
959:
550:
In 2014, it was shown that magnetic components, like the ones in
524:
of particle physics. The effect was reported by researchers at
381:
24:
6785:
5736:"Nanometric holograms based on a topological insulator material"
4360:
Kushwaha, S. K.; Pletikosić, I.; Liang, T.; et al. (2015).
2862:"$ {Z}_{2}$ Topological Order and the Quantum Spin Hall Effect"
34:
reads like a scientific review article and potentially contains
7646:
7641:
7247:
5859:
5023:"Periodic table for topological insulators and superconductors"
5021:
Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail (2009).
4374:
S bulk crystal topological insulator with excellent properties"
2605:
Pankratov, O. A.; Pakhomov, S. V.; Volkov, B. A. (1987-01-01).
2255:"Periodic table for topological insulators and superconductors"
963:
166:
165:
of a topological insulator with a trivial insulator (including
145:
A topological insulator is an insulator for the same reason a "
1880:
Moore, Joel E. (2010). "The birth of topological insulators".
7621:
7242:
6848:
Ginley, Theresa P.; Wang, Yong; Law, Stephanie (2016-11-23).
6831:
Text was copied from this source, which is available under a
6827:
780:
discovered in 1991.) More generally (in what is known as the
521:
3923:"2D layered transport properties from topological insulator
3671:
Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; et al. (2009).
3042:
928:(PVD), solvothermal synthesis, sonochemical technique and
878:
Some of the most well-known topological insulators are also
122:
for a 3D time-reversal symmetric topological insulator. The
16:
State of matter with insulating bulk but conductive boundary
5545:
4228:
3858:"Molecular Beam Epitaxial Growth of Topological Insulators"
2581:"Two-dimensional massless electrons in an inverted contact"
1243:
is usually terminated by Te due to its low surface energy.
207:
5790:
5397:
7252:
4828:
4139:
2659:"Quantum Spin Hall Insulator State in HgTe Quantum Wells"
2320:"Symmetry-Protected Topological Phases of Quantum Matter"
6602:
5142:
4955:
4250:
observed by angle-resolved photoemission spectroscopy".
2058:
6362:"Topological Insulators: Fundamentals and Perspectives"
5020:
4727:
3920:
3539:
2604:
1120:
1069:
426:, and many other measurements, it was observed that Bi
218:. So-called "topological invariants", taking values in
6833:
Creative Commons Attribution 4.0 International License
4683:(7428). Springer Science and Business Media LLC: 165.
2656:
6960:
6445:
5833:
Are Topological Insulators Promising Thermoelectrics?
3608:
2795:
Bernevig, B. Andrei; Zhang, Shou-Cheng (2006-03-14).
2455:
1996:
Topological Order and the Quantum Spin Hall Effect".
1716:
816:
794:
754:
719:
689:
660:
631:
602:
349:
253:
224:
87:
6389:
He, Liang; Kou, Xufeng; Wang, Kang L. (2013-01-31).
5830:
Toriyama, Michael; Snyder, G. Jeffrey (2023-11-06),
5793:"The Thermoelectric Properties of Bismuth Telluride"
4491:
6312:
4611:
2924:
7009:
6468:film on Si(111) with atomically sharp interface".
5598:
5077:
4569:(18). American Physical Society (APS): 1799–1802.
1731:
831:
802:
769:
734:
704:
675:
646:
617:
364:
261:
239:
210:from particle number conservation, and often have
102:
6175:thin films on dielectric amorphous SiO2 by MBE".
5145:"Exploring topological phases with quantum walks"
565:
547:, which is a bulk insulator at low temperatures.
485:. Many semiconductors within the large family of
7785:
7185:"The Strange Topology That Is Reshaping Physics"
3743:
3670:
3217:
3156:
2119:Qi, Xiao-Liang; Zhang, Shou-Cheng (2011-10-14).
1808:synthesized materials. One of the candidates is
7145:Proceedings of the National Academy of Sciences
6528:
6153:
4439:(19). American Physical Society (APS): 195424.
4296:
3821:, John Wiley & Sons, Ltd, pp. 55–100,
2578:
1991:
7047:
6904:
6246:
5829:
5668:
4736:(2010-03-12). "Topological Kondo Insulators".
3816:
2600:
2598:
2579:Volkov, B. A.; Pankratov, O. A. (1985-08-25).
654:invariants. An experimental method to measure
578:
7211:
6847:
6682:
5733:
4806:"Weird materials could make faster computers"
4430:
4355:
4353:
2794:
7225:
6110:
6011:: CS1 maint: multiple names: authors list (
5271:
4670:
3103:
2121:"Topological insulators and superconductors"
324:group in 2D topological insulators in 2007.
202:, and can be classified using the so-called
6025:
5459:
5078:Panahiyan, S.; Fritzsche, S. (2021-01-05).
3855:
2595:
2574:
2572:
938:Schematic of the components of a MBE system
391:
149:" (ordinary) insulator is: there exists an
134:is a material whose interior behaves as an
7301:
7218:
7204:
4350:
3666:
3664:
3662:
3609:Hasan, M. Zahid; Kane, Charles L. (2010).
3317:
2652:
2650:
2648:
1938:
1763:Mathematically, this assignment creates a
7166:
7156:
7093:
7010:Kane, Charles L.; Moore, Joel E. (2011).
6976:
6918:
6865:
6811:
6738:
6725:with highly tunable chemical potential".
6659:
6641:
6563:
6481:
6414:
6388:
6260:
6188:
5964:
5894:
5767:
5710:
5613:
5559:
5412:
5350:
5336:
5289:
5248:
5230:
5160:
5095:
5038:
4973:
4908:
4843:
4749:
4696:
4647:
4629:
4505:
4444:
4407:
4389:
4317:
4263:
4092:
4030:
3993:
3959:
3881:
3761:
3688:
3626:
3553:
3492:
3396:
3331:
3320:Annual Review of Condensed Matter Physics
3275:
3170:
3117:
3056:
3011:
2942:
2877:
2812:
2747:
2674:
2528:
2510:
2400:
2335:
2324:Annual Review of Condensed Matter Physics
2270:
2204:
2186:
2136:
2092:
2011:
1952:
1941:Annual Review of Condensed Matter Physics
1719:
1435:Lattice mismatch of different substrates
819:
796:
757:
722:
692:
663:
634:
605:
479:angle-resolved photoemission spectroscopy
424:angle-resolved photoemission spectroscopy
352:
255:
227:
90:
62:Learn how and when to remove this message
7110:
7075:
4897:Journal of the Physical Society of Japan
3478:
3350:10.1146/annurev-conmatphys-062910-140432
2859:
2729:
2569:
2354:10.1146/annurev-conmatphys-031214-014740
2187:Hasan, M. Z.; Kane, C. L. (2010-11-08).
1971:10.1146/annurev-conmatphys-062910-140432
1852:Periodic table of topological invariants
1797:periodic table of topological insulators
1749:Periodic table of topological invariants
933:
841:periodic table of topological invariants
712:topological order. (Note that the term
422:with a small electronic band gap. Using
204:periodic table of topological insulators
195:that defines ordinary states of matter.
113:
75:
7078:"Topological insulators: Star material"
5212:
4560:
3659:
2860:Kane, C. L.; Mele, E. J. (2005-09-28).
2730:Kane, C. L.; Mele, E. J. (2005-11-23).
2645:
2317:
2118:
920:metal-organic chemical vapor deposition
7786:
5330:
5213:Khazali, Mohammadsadegh (2022-03-03).
3261:
2732:"Quantum Spin Hall Effect in Graphene"
2252:
1802:
295:topological insulators, among others.
7199:
7138:
7125:
6843:
6841:
6384:
6382:
6356:
6354:
6352:
6308:
6306:
6304:
6242:
6240:
5208:
5206:
5204:
3851:
3849:
3847:
3845:
3313:
3311:
2248:
2246:
2244:
2242:
2240:
2182:
2180:
2114:
2112:
1879:
1739:topology by definition of the state.
7742:
4890:
3443:
2189:"Colloquium: Topological insulators"
1121:Bismuth-based topological insulators
1070:PVD growth of topological insulators
954:MBE growth of topological insulators
216:symmetry-protected topological order
18:
7766:
5502:
2997:
1992:Kane, C. L.; Mele, E. J. (2005). "Z
958:Molecular beam epitaxy (MBE) is an
744:has also been used to describe the
13:
6954:
6838:
6379:
6349:
6301:
6237:
5201:
3842:
3308:
3255:
3218:Kane, C. L.; Moore, J. E. (2011).
2237:
2177:
2109:
873:
438:(SS) crossing between any pair of
418:. Bismuth in its pure state, is a
14:
7810:
7113:"Focus on Topological Insulators"
4893:"Topological Insulator Materials"
3944:single crystals and micro flakes"
2458:"Magnetic topological insulators"
2385:"Photonic topological insulators"
1985:
1932:
1873:
1791:; an anti-unitary operator which
1742:
1704:
1288:can be grown on top of various Bi
458:in 2D graphene and pure bismuth.
400:quantum wells sandwiched between
7765:
7753:
7741:
7730:
7729:
6826:
4958:"Floquet topological insulators"
1832:Topological quantum field theory
1732:{\displaystyle \mathbb {Z} _{2}}
839:or trivial) as described by the
832:{\displaystyle \mathbb {Z} _{2}}
770:{\displaystyle \mathbb {Z} _{2}}
735:{\displaystyle \mathbb {Z} _{2}}
705:{\displaystyle \mathbb {Z} _{2}}
676:{\displaystyle \mathbb {Z} _{2}}
647:{\displaystyle \mathbb {Z} _{2}}
618:{\displaystyle \mathbb {Z} _{2}}
365:{\displaystyle \mathbb {Z} _{2}}
240:{\displaystyle \mathbb {Z} _{2}}
138:while its surface behaves as an
103:{\displaystyle \mathbb {Z} _{2}}
23:
6929:10.1016/j.commatsci.2012.12.013
6907:Computational Materials Science
6898:
6874:
6779:
6676:
6596:
6522:
6439:
6147:
6104:
6019:
5943:
5853:
5823:
5784:
5727:
5662:
5592:
5539:
5496:
5453:
5391:
5265:
5136:
5071:
5014:
4949:
4884:
4822:
4798:
4721:
4664:
4605:
4554:
4485:
4424:
4222:
4133:
4071:
4010:
3914:
3810:
3737:
3602:
3533:
3472:
3437:
3372:
3211:
3150:
3097:
3036:
2991:
2918:
2853:
2788:
2723:
2504:
2449:
898:(n-type thermoelectrics) and Sb
193:Landau symmetry-breaking theory
6133:10.1016/j.jcrysgro.2004.08.015
5308:10.1103/PhysRevLett.100.096407
4768:10.1103/physrevlett.104.106408
4671:Samuel Reich, Eugenie (2012).
4524:10.1103/physrevlett.102.146805
4208:10.1103/PhysRevLett.103.146401
2376:
2311:
2052:
1862:Photonic topological insulator
566:Floquet topological insulators
543:insulators were identified in
456:quantum Hall fractionalization
450:has been predicted to have 3D
1:
7328:Spontaneous symmetry breaking
6090:10.1016/S0022-0248(03)01019-4
5797:Advanced Electronic Materials
3511:10.1103/PhysRevLett.95.226801
3075:10.1103/PhysRevLett.98.106803
2896:10.1103/PhysRevLett.95.146802
2831:10.1103/PhysRevLett.96.106802
2766:10.1103/PhysRevLett.95.226801
2253:Kitaev, Alexei (2009-05-14).
2030:10.1103/PhysRevLett.95.146802
1867:
992:scanning tunneling microscopy
860:quantum anomalous Hall effect
298:
7126:Moore, Joel E. (July 2011).
5983:10.1021/acs.nanolett.6b05260
5842:10.26434/chemrxiv-2023-3nvl3
5578:10.1103/RevModPhys.88.035005
2631:10.1016/0038-1098(87)90934-3
1827:Topological quantum computer
1770:Specifically, the number of
913:
803:{\displaystyle \mathbb {Z} }
496:two-dimensional electron gas
262:{\displaystyle \mathbb {Z} }
155:valence and conduction bands
7:
6605:"Coherent heteroepitaxy of
5482:10.1103/physrevlett.66.1773
5272:Fu, L.; C. L. Kane (2008).
5114:10.1103/physreva.103.012201
4891:Ando, Yoichi (2013-10-15).
4583:10.1103/physrevlett.58.1799
1815:
579:Properties and applications
556:metal–insulator transitions
552:spin-torque computer memory
10:
7815:
7508:Spin gapless semiconductor
7417:Nearly free electron model
7111:Murakami, Shuichi (2010).
7053:. Wiley. pp. 55–100.
7041:10.1088/2058-7058/24/02/36
6995:10.1103/RevModPhys.82.3045
6335:10.1038/natrevmats.2017.49
5369:10.1103/physrevb.85.094516
5179:10.1103/physreva.82.033429
5027:AIP Conference Proceedings
4463:10.1103/physrevb.78.195424
4282:10.1209/0295-5075/81/57006
3645:10.1103/RevModPhys.82.3045
3294:10.1103/PhysRevB.76.045302
3249:10.1088/2058-7058/24/02/36
3136:10.1103/PhysRevB.76.045302
3022:10.1103/PhysRevB.79.195322
2797:"Quantum Spin Hall Effect"
2611:Solid State Communications
2318:Senthil, T. (2015-03-01).
2259:AIP Conference Proceedings
2223:10.1103/RevModPhys.82.3045
2155:10.1103/RevModPhys.83.1057
2085:10.1103/PhysRevB.85.235401
1837:Topological quantum number
1746:
7725:
7687:
7612:
7556:
7516:
7465:
7457:Density functional theory
7432:electronic band structure
7399:
7348:
7341:
7310:
7299:
7233:
7059:10.1002/9783527681594.ch4
6964:Reviews of Modern Physics
6813:10.1038/s43246-020-0037-y
6500:10.1016/j.tsf.2011.07.033
6395:Physica Status Solidi RRL
6113:Journal of Crystal Growth
6070:Journal of Crystal Growth
5250:10.22331/q-2022-03-03-664
4962:Physica Status Solidi RRL
3827:10.1002/9783527681594.ch4
3615:Reviews of Modern Physics
3189:10.1088/1367-2630/9/9/356
2482:10.1038/s42254-018-0011-5
2193:Reviews of Modern Physics
2125:Reviews of Modern Physics
926:physical vapor deposition
7794:Condensed matter physics
7627:Bogoliubov quasiparticle
7371:Quantum spin Hall effect
7263:Bose–Einstein condensate
7227:Condensed matter physics
7128:"Topological Insulators"
7012:"Topological Insulators"
6792:Communications Materials
6315:Nature Reviews Materials
5525:10.1103/physrevb.44.2664
4728:Dzero, Maxim; Sun, Kai;
3611:"Topological Insulators"
3220:"Topological Insulators"
1847:Quantum spin Hall effect
1787:which commutes with the
1300:buffers. Table 1 shows
1218:thermoelectric materials
1129:based materials such as
880:thermoelectric materials
526:Johns Hopkins University
392:Experimental realization
7158:10.1073/pnas.1611504113
6630:Applied Physics Letters
6552:Applied Physics Letters
5632:10.1126/science.1234414
5431:10.1126/science.1167733
4738:Physical Review Letters
4649:10.1126/science.aaf5541
4563:Physical Review Letters
4494:Physical Review Letters
4188:Physical Review Letters
3780:10.1126/science.1167733
3572:10.1126/science.1146509
3481:Physical Review Letters
3466:10.1103/PhysRevA.8.1570
3045:Physical Review Letters
2961:10.1126/science.1133734
2866:Physical Review Letters
2801:Physical Review Letters
2736:Physical Review Letters
2693:10.1126/science.1148047
1999:Physical Review Letters
386:quantum spin Hall state
7118:New Journal of Physics
7051:Topological Insulators
6416:10.1002/pssr.201307003
5809:10.1002/aelm.201800904
5695:10.1126/sciadv.1501536
4992:10.1002/pssr.201206451
4927:10.7566/jpsj.82.102001
3883:10.1002/adma.201003855
3819:Topological Insulators
3159:New Journal of Physics
2462:Nature Reviews Physics
1810:half-Heusler compounds
1733:
939:
930:molecular beam epitaxy
890:and its alloys with Bi
833:
804:
771:
736:
706:
677:
648:
619:
590:helical Dirac fermions
434:alloy exhibits an odd
366:
322:Laurens W. Molenkamp's
263:
241:
212:time-reversal symmetry
127:
111:
104:
7503:Topological insulator
7437:Anderson localization
7076:Brumfiel, G. (2010).
5740:Nature Communications
4378:Nature Communications
1785:anti-unitary operator
1734:
937:
834:
805:
772:
737:
707:
678:
649:
620:
539:In 2012, topological
367:
335:in 2005, and also by
264:
242:
191:not described by the
132:topological insulator
117:
105:
79:
7381:Aharonov–Bohm effect
7268:Fermionic condensate
6867:10.3390/cryst6110154
1772:connected components
1714:
814:
792:
752:
717:
687:
658:
629:
600:
347:
251:
222:
140:electrical conductor
136:electrical insulator
85:
7772:Physics WikiProject
7447:tight binding model
7427:Fermi liquid theory
7412:Free electron model
7361:Quantum Hall effect
7342:Electrons in solids
7189:Scientific American
7033:2011PhyW...24b..32K
6987:2010RvMP...82.3045H
6804:2020CoMat...1...38S
6749:2010NanoL..10.2245K
6652:2010ApPhL..97z2104R
6574:2009ApPhL..95e3114Z
6492:2011TSF...520..224B
6407:2013PSSRR...7...50H
6327:2017NatRM...217049H
6271:10.1038/nature12385
6199:2013Nanos...510618J
6125:2004JCrGr.271..456C
6082:2003JCrGr.253..445W
5975:2017NanoL..17.2354T
5905:2012NanoL..12.4711A
5760:10.1038/ncomms15354
5752:2017NatCo...815354Y
5687:2016SciA....2E1536Y
5624:2013Sci...340..167C
5570:2016RvMP...88c5005C
5517:1991PhRvB..44.2664W
5474:1991PhRvL..66.1773R
5423:2009Sci...323..919H
5361:2012PhRvB..85i4516P
5300:2008PhRvL.100i6407F
5241:2022Quant...6..664K
5171:2010PhRvA..82c3429K
5106:2021PhRvA.103a2201P
5049:2009AIPC.1134...22K
4984:2013PSSRR...7..101C
4919:2013JPSJ...82j2001A
4862:10.1038/nature13534
4854:2014Natur.511..449M
4760:2010PhRvL.104j6408D
4689:2012Natur.492..165S
4640:2016Sci...354.1124W
4575:1987PhRvL..58.1799W
4516:2009PhRvL.102n6805E
4455:2008PhRvB..78s5424Q
4400:10.1038/ncomms11456
4328:2014NatPh..10..956X
4274:2008EL.....8157006N
4200:2009PhRvL.103n6401H
4103:2010NatMa...9..546L
4041:2010NatMa...9..541C
3970:2016NatSR...627483C
3874:2011AdM....23.1162C
3772:2009Sci...323..919H
3707:10.1038/nature08234
3699:2009Natur.460.1101H
3637:2010RvMP...82.3045H
3564:2007Sci...317.1729B
3503:2005PhRvL..95v6801K
3458:1973PhRvA...8.1570B
3415:10.1038/nature06843
3407:2008Natur.452..970H
3342:2011ARCMP...2...55H
3286:2007PhRvB..76d5302F
3241:2011PhyW...24b..32K
3181:2007NJPh....9..356M
3128:2007PhRvB..76d5302F
3067:2007PhRvL..98j6803F
2953:2006Sci...314.1757B
2937:(5806): 1757–1761.
2888:2005PhRvL..95n6802K
2823:2006PhRvL..96j6802B
2758:2005PhRvL..95v6801K
2685:2007Sci...318..766K
2623:1987SSCom..61...93P
2539:2016NatPh..12.1124H
2474:2019NatRP...1..126T
2411:2013NatMa..12..233K
2346:2015ARCMP...6..299S
2281:2009AIPC.1134...22K
2215:2010RvMP...82.3045H
2147:2011RvMP...83.1057Q
2077:2012PhRvB..85w5401Z
2022:2005PhRvL..95n6802K
1963:2011ARCMP...2...55H
1902:10.1038/nature08916
1894:2010Natur.464..194M
1842:Quantum Hall effect
1803:Future developments
1436:
948:integrated circuits
908:Seebeck coefficient
856:quantum Hall effect
786:random Hamiltonians
594:quantum Hall effect
545:samarium hexaboride
278:"U"-turn scattering
7333:Critical phenomena
7139:Ornes, S. (2016).
6207:10.1039/C3NR03032F
3948:Scientific Reports
3862:Advanced Materials
1729:
1434:
940:
829:
800:
767:
732:
702:
673:
644:
615:
585:Majorana particles
560:Bose–Hubbard model
530:Rutgers University
475:antimony telluride
362:
337:B. Andrei Bernevig
259:
237:
128:
112:
100:
7781:
7780:
7667:Exciton-polariton
7552:
7551:
7524:Thermoelectricity
6757:10.1021/nl101260j
6661:10.1063/1.3532845
6582:10.1063/1.3200237
6255:(7459): 419–425.
5913:10.1021/nl302108r
5608:(6129): 167–170.
5554:(35005): 035005.
5407:(5916): 919–922.
5339:Physical Review B
5149:Physical Review A
5084:Physical Review A
5057:10.1063/1.3149495
5033:(1). AIP: 22–30.
4838:(7510): 449–451.
4433:Physical Review B
4336:10.1038/nphys3140
3978:10.1038/srep27483
3836:978-3-527-68159-4
3756:(5916): 919–922.
3548:(5845): 1729–31.
3446:Physical Review A
3264:Physical Review B
3106:Physical Review B
3000:Physical Review B
2669:(5851): 766–770.
2547:10.1038/nphys3867
2523:(12): 1124–1129.
2289:10.1063/1.3149495
2065:Physical Review B
1888:(7286): 194–198.
1822:Topological order
1783:respectively: an
1702:
1701:
968:ultra-high vacuum
864:magnetoelectronic
852:quantum computers
746:topological order
742:topological order
487:Heusler materials
471:bismuth telluride
402:cadmium telluride
72:
71:
64:
7806:
7769:
7768:
7757:
7745:
7744:
7733:
7732:
7672:Phonon polariton
7564:Amorphous magnet
7544:Electrostriction
7539:Flexoelectricity
7534:Ferroelectricity
7529:Piezoelectricity
7386:Josephson effect
7366:Spin Hall effect
7346:
7345:
7323:Phase transition
7305:
7288:Luttinger liquid
7235:States of matter
7220:
7213:
7206:
7197:
7196:
7192:
7180:
7170:
7160:
7135:
7122:
7107:
7097:
7072:
7044:
7016:
7006:
6980:
6949:
6948:
6922:
6902:
6896:
6895:
6893:
6892:
6878:
6872:
6871:
6869:
6845:
6836:
6830:
6825:
6815:
6783:
6777:
6776:
6742:
6724:
6723:
6722:
6714:
6713:
6703:
6702:
6701:
6693:
6692:
6680:
6674:
6673:
6663:
6645:
6625:
6624:
6623:
6615:
6614:
6600:
6594:
6593:
6567:
6549:
6548:
6547:
6539:
6538:
6526:
6520:
6519:
6485:
6470:Thin Solid Films
6467:
6466:
6465:
6457:
6456:
6443:
6437:
6436:
6418:
6386:
6377:
6376:
6374:
6373:
6358:
6347:
6346:
6310:
6299:
6298:
6264:
6244:
6235:
6234:
6192:
6183:(21): 10618–22.
6174:
6173:
6172:
6164:
6163:
6151:
6145:
6144:
6119:(3–4): 456–461.
6108:
6102:
6101:
6076:(1–4): 445–451.
6067:
6066:
6065:
6057:
6056:
6046:
6045:
6044:
6036:
6035:
6023:
6017:
6016:
6010:
6002:
5968:
5947:
5941:
5940:
5898:
5880:
5879:
5878:
5870:
5869:
5857:
5851:
5850:
5849:
5848:
5827:
5821:
5820:
5788:
5782:
5781:
5771:
5731:
5725:
5724:
5714:
5675:Science Advances
5666:
5660:
5659:
5617:
5596:
5590:
5589:
5563:
5543:
5537:
5536:
5511:(6): 2664–2672.
5500:
5494:
5493:
5457:
5451:
5450:
5416:
5395:
5389:
5388:
5354:
5334:
5328:
5327:
5293:
5269:
5263:
5262:
5252:
5234:
5210:
5199:
5198:
5164:
5140:
5134:
5133:
5099:
5075:
5069:
5068:
5042:
5018:
5012:
5011:
4977:
4968:(1–2): 101–108.
4953:
4947:
4946:
4912:
4888:
4882:
4881:
4847:
4826:
4820:
4819:
4817:
4816:
4802:
4796:
4795:
4753:
4730:Galitski, Victor
4725:
4719:
4718:
4700:
4668:
4662:
4661:
4651:
4633:
4624:(6316): 1124–7.
4609:
4603:
4602:
4558:
4552:
4551:
4509:
4489:
4483:
4482:
4448:
4428:
4422:
4421:
4411:
4393:
4357:
4348:
4347:
4321:
4300:
4294:
4293:
4267:
4249:
4248:
4247:
4239:
4238:
4226:
4220:
4219:
4183:
4182:
4181:
4173:
4172:
4162:
4161:
4160:
4152:
4151:
4137:
4131:
4130:
4111:10.1038/nmat2771
4096:
4075:
4069:
4068:
4049:10.1038/nmat2770
4034:
4019:Nature Materials
4014:
4008:
4007:
3997:
3963:
3943:
3942:
3941:
3933:
3932:
3918:
3912:
3911:
3885:
3853:
3840:
3839:
3814:
3808:
3807:
3765:
3741:
3735:
3734:
3692:
3683:(7259): 1101–5.
3668:
3657:
3656:
3630:
3606:
3600:
3599:
3557:
3537:
3531:
3530:
3496:
3494:cond-mat/0411737
3476:
3470:
3469:
3441:
3435:
3434:
3400:
3376:
3370:
3369:
3335:
3315:
3306:
3305:
3279:
3277:cond-mat/0611341
3259:
3253:
3252:
3224:
3215:
3209:
3208:
3174:
3154:
3148:
3147:
3121:
3119:cond-mat/0611341
3101:
3095:
3094:
3060:
3058:cond-mat/0607699
3040:
3034:
3033:
3015:
3013:cond-mat/0607531
2995:
2989:
2988:
2946:
2944:cond-mat/0611399
2922:
2916:
2915:
2881:
2879:cond-mat/0506581
2857:
2851:
2850:
2816:
2814:cond-mat/0504147
2792:
2786:
2785:
2751:
2749:cond-mat/0411737
2727:
2721:
2720:
2678:
2654:
2643:
2642:
2602:
2593:
2592:
2576:
2567:
2566:
2532:
2508:
2502:
2501:
2453:
2447:
2446:
2419:10.1038/nmat3520
2404:
2389:Nature Materials
2380:
2374:
2373:
2339:
2315:
2309:
2308:
2274:
2250:
2235:
2234:
2208:
2199:(4): 3045–3067.
2184:
2175:
2174:
2140:
2131:(4): 1057–1110.
2116:
2107:
2106:
2096:
2056:
2050:
2049:
2015:
2013:cond-mat/0506581
1989:
1983:
1982:
1956:
1936:
1930:
1929:
1877:
1857:Bismuth selenide
1738:
1736:
1735:
1730:
1728:
1727:
1722:
1689:
1688:
1687:
1665:
1664:
1663:
1655:
1654:
1618:
1617:
1616:
1552:
1551:
1550:
1508:
1507:
1506:
1498:
1497:
1485:
1484:
1483:
1475:
1474:
1462:
1461:
1460:
1452:
1451:
1437:
1433:
1430:
1429:
1428:
1420:
1419:
1409:
1408:
1407:
1399:
1398:
1388:
1387:
1386:
1378:
1377:
1366:
1364:
1363:
1355:
1354:
1343:
1342:
1341:
1333:
1332:
1322:
1320:
1319:
1311:
1310:
1287:
1286:
1285:
1277:
1276:
1266:
1265:
1264:
1256:
1255:
1242:
1240:
1239:
1231:
1230:
1191:
1190:
1189:
1181:
1180:
1170:
1169:
1168:
1160:
1159:
1149:
1148:
1147:
1139:
1138:
1116:
1115:
1114:
1106:
1105:
1095:
1094:
1093:
1085:
1084:
1065:
1063:
1062:
1054:
1053:
1045:
1044:
1019:
1017:
1016:
1008:
1007:
983:lattice mismatch
838:
836:
835:
830:
828:
827:
822:
809:
807:
806:
801:
799:
776:
774:
773:
768:
766:
765:
760:
741:
739:
738:
733:
731:
730:
725:
711:
709:
708:
703:
701:
700:
695:
682:
680:
679:
674:
672:
671:
666:
653:
651:
650:
645:
643:
642:
637:
624:
622:
621:
616:
614:
613:
608:
534:THz spectroscopy
483:bismuth selenide
467:bismuth selenide
371:
369:
368:
363:
361:
360:
355:
268:
266:
265:
260:
258:
246:
244:
243:
238:
236:
235:
230:
109:
107:
106:
101:
99:
98:
93:
67:
60:
56:
27:
19:
7814:
7813:
7809:
7808:
7807:
7805:
7804:
7803:
7784:
7783:
7782:
7777:
7721:
7702:Granular matter
7697:Amorphous solid
7683:
7608:
7594:Antiferromagnet
7584:Superparamagnet
7557:Magnetic phases
7548:
7512:
7461:
7422:Bloch's theorem
7395:
7337:
7318:Order parameter
7311:Phase phenomena
7306:
7297:
7229:
7224:
7183:
7151:(37): 10223–4.
7095:10.1038/466310a
7088:(7304): 310–1.
7084:(Nature News).
7069:
7014:
6957:
6955:Further reading
6952:
6903:
6899:
6890:
6888:
6886:topocondmat.org
6880:
6879:
6875:
6846:
6839:
6784:
6780:
6721:
6718:
6717:
6716:
6712:
6709:
6708:
6707:
6705:
6700:
6697:
6696:
6695:
6691:
6688:
6687:
6686:
6684:
6681:
6677:
6626:on GaAs (111)B"
6622:
6619:
6618:
6617:
6613:
6610:
6609:
6608:
6606:
6601:
6597:
6546:
6543:
6542:
6541:
6537:
6534:
6533:
6532:
6530:
6527:
6523:
6464:
6461:
6460:
6459:
6455:
6452:
6451:
6450:
6448:
6444:
6440:
6387:
6380:
6371:
6369:
6360:
6359:
6350:
6311:
6302:
6245:
6238:
6171:
6168:
6167:
6166:
6162:
6159:
6158:
6157:
6155:
6152:
6148:
6109:
6105:
6068:nanocrystals".
6064:
6061:
6060:
6059:
6055:
6052:
6051:
6050:
6048:
6047:and flake-like
6043:
6040:
6039:
6038:
6034:
6031:
6030:
6029:
6027:
6024:
6020:
6004:
6003:
5948:
5944:
5877:
5874:
5873:
5872:
5868:
5865:
5864:
5863:
5861:
5858:
5854:
5846:
5844:
5828:
5824:
5789:
5785:
5746:: ncomms15354.
5732:
5728:
5681:(3): e1501536.
5667:
5663:
5597:
5593:
5544:
5540:
5501:
5497:
5462:Phys. Rev. Lett
5458:
5454:
5396:
5392:
5335:
5331:
5278:Phys. Rev. Lett
5270:
5266:
5211:
5202:
5141:
5137:
5076:
5072:
5019:
5015:
4954:
4950:
4889:
4885:
4827:
4823:
4814:
4812:
4804:
4803:
4799:
4726:
4722:
4698:10.1038/492165a
4669:
4665:
4610:
4606:
4559:
4555:
4490:
4486:
4429:
4425:
4373:
4369:
4365:
4358:
4351:
4312:(12): 956–963.
4301:
4297:
4246:
4243:
4242:
4241:
4237:
4234:
4233:
4232:
4230:
4227:
4223:
4180:
4177:
4176:
4175:
4171:
4168:
4167:
4166:
4164:
4159:
4156:
4155:
4154:
4150:
4147:
4146:
4145:
4143:
4138:
4134:
4076:
4072:
4015:
4011:
3940:
3937:
3936:
3935:
3931:
3928:
3927:
3926:
3924:
3919:
3915:
3854:
3843:
3837:
3815:
3811:
3742:
3738:
3669:
3660:
3607:
3603:
3538:
3534:
3477:
3473:
3442:
3438:
3377:
3373:
3316:
3309:
3260:
3256:
3222:
3216:
3212:
3155:
3151:
3102:
3098:
3041:
3037:
2996:
2992:
2923:
2919:
2858:
2854:
2793:
2789:
2728:
2724:
2655:
2646:
2603:
2596:
2577:
2570:
2509:
2505:
2454:
2450:
2381:
2377:
2316:
2312:
2251:
2238:
2185:
2178:
2117:
2110:
2057:
2053:
1995:
1990:
1986:
1937:
1933:
1878:
1874:
1870:
1818:
1805:
1754:Bloch's theorem
1751:
1745:
1723:
1718:
1717:
1715:
1712:
1711:
1707:
1686:
1683:
1682:
1681:
1679:
1662:
1659:
1658:
1657:
1653:
1650:
1649:
1648:
1646:
1615:
1612:
1611:
1610:
1608:
1549:
1546:
1545:
1544:
1542:
1505:
1502:
1501:
1500:
1496:
1493:
1492:
1491:
1489:
1482:
1479:
1478:
1477:
1473:
1470:
1469:
1468:
1466:
1459:
1456:
1455:
1454:
1450:
1447:
1446:
1445:
1443:
1427:
1424:
1423:
1422:
1418:
1415:
1414:
1413:
1411:
1406:
1403:
1402:
1401:
1397:
1394:
1393:
1392:
1390:
1385:
1382:
1381:
1380:
1376:
1373:
1372:
1371:
1369:
1362:
1359:
1358:
1357:
1353:
1350:
1349:
1348:
1345:
1340:
1337:
1336:
1335:
1331:
1328:
1327:
1326:
1324:
1318:
1315:
1314:
1313:
1309:
1306:
1305:
1304:
1301:
1299:
1295:
1291:
1284:
1281:
1280:
1279:
1275:
1272:
1271:
1270:
1268:
1263:
1260:
1259:
1258:
1254:
1251:
1250:
1249:
1247:
1238:
1235:
1234:
1233:
1229:
1226:
1225:
1224:
1221:
1214:
1210:
1206:
1201:
1197:
1188:
1185:
1184:
1183:
1179:
1176:
1175:
1174:
1172:
1167:
1164:
1163:
1162:
1158:
1155:
1154:
1153:
1151:
1146:
1143:
1142:
1141:
1137:
1134:
1133:
1132:
1130:
1123:
1113:
1110:
1109:
1108:
1104:
1101:
1100:
1099:
1097:
1092:
1089:
1088:
1087:
1083:
1080:
1079:
1078:
1076:
1072:
1061:
1058:
1057:
1056:
1052:
1049:
1048:
1047:
1043:
1040:
1039:
1038:
1035:
1015:
1012:
1011:
1010:
1006:
1003:
1002:
1001:
998:
994:(STM) studies.
976:single crystals
944:heterostructure
916:
905:
901:
897:
893:
889:
885:
876:
874:Thermoelectrics
823:
818:
817:
815:
812:
811:
795:
793:
790:
789:
761:
756:
755:
753:
750:
749:
726:
721:
720:
718:
715:
714:
696:
691:
690:
688:
685:
684:
667:
662:
661:
659:
656:
655:
638:
633:
632:
630:
627:
626:
609:
604:
603:
601:
598:
597:
581:
568:
518:magnetoelectric
512:
508:
504:
452:Dirac particles
449:
445:
433:
429:
416:
412:
394:
356:
351:
350:
348:
345:
344:
341:Shoucheng Zhang
329:Charles L. Kane
301:
254:
252:
249:
248:
231:
226:
225:
223:
220:
219:
189:state of matter
94:
89:
88:
86:
83:
82:
68:
57:
54:(February 2024)
47:
43:primary sources
28:
17:
12:
11:
5:
7812:
7802:
7801:
7799:Semiconductors
7796:
7779:
7778:
7776:
7775:
7763:
7760:Physics Portal
7751:
7739:
7726:
7723:
7722:
7720:
7719:
7714:
7709:
7707:Liquid crystal
7704:
7699:
7693:
7691:
7685:
7684:
7682:
7681:
7676:
7675:
7674:
7669:
7659:
7654:
7649:
7644:
7639:
7634:
7629:
7624:
7618:
7616:
7614:Quasiparticles
7610:
7609:
7607:
7606:
7601:
7596:
7591:
7586:
7581:
7576:
7574:Superdiamagnet
7571:
7566:
7560:
7558:
7554:
7553:
7550:
7549:
7547:
7546:
7541:
7536:
7531:
7526:
7520:
7518:
7514:
7513:
7511:
7510:
7505:
7500:
7498:Superconductor
7495:
7490:
7485:
7480:
7478:Mott insulator
7475:
7469:
7467:
7463:
7462:
7460:
7459:
7454:
7449:
7444:
7439:
7434:
7429:
7424:
7419:
7414:
7409:
7403:
7401:
7397:
7396:
7394:
7393:
7388:
7383:
7378:
7373:
7368:
7363:
7358:
7352:
7350:
7343:
7339:
7338:
7336:
7335:
7330:
7325:
7320:
7314:
7312:
7308:
7307:
7300:
7298:
7296:
7295:
7290:
7285:
7280:
7275:
7270:
7265:
7260:
7255:
7250:
7245:
7239:
7237:
7231:
7230:
7223:
7222:
7215:
7208:
7200:
7194:
7193:
7181:
7136:
7123:
7108:
7073:
7067:
7045:
7007:
6971:(4): 3045–67.
6956:
6953:
6951:
6950:
6897:
6873:
6837:
6778:
6733:(6): 2245–50.
6719:
6710:
6698:
6689:
6675:
6636:(26): 262104.
6620:
6611:
6595:
6544:
6535:
6521:
6462:
6453:
6438:
6401:(1–2): 50–63.
6378:
6348:
6300:
6236:
6169:
6160:
6146:
6103:
6062:
6053:
6041:
6032:
6018:
5959:(4): 2354–60.
5942:
5875:
5866:
5852:
5822:
5783:
5726:
5661:
5591:
5548:Rev. Mod. Phys
5538:
5495:
5468:(13): 1773–6.
5452:
5390:
5329:
5264:
5200:
5135:
5070:
5013:
4948:
4903:(10): 102001.
4883:
4821:
4797:
4744:(10): 106408.
4734:Coleman, Piers
4720:
4663:
4604:
4553:
4500:(14): 146805.
4484:
4423:
4371:
4367:
4363:
4349:
4306:Nature Physics
4295:
4244:
4235:
4221:
4194:(14): 146401.
4178:
4169:
4157:
4148:
4132:
4070:
4009:
3938:
3929:
3913:
3841:
3835:
3809:
3736:
3658:
3621:(4): 3045–67.
3601:
3532:
3487:(22): 226801.
3471:
3452:(3): 1570–81.
3436:
3381:M. Zahid Hasan
3371:
3307:
3254:
3210:
3149:
3096:
3051:(10): 106803.
3035:
2990:
2917:
2872:(14): 146802.
2852:
2807:(10): 106802.
2787:
2742:(22): 226801.
2722:
2644:
2594:
2568:
2517:Nature Physics
2503:
2468:(2): 126–143.
2448:
2395:(3): 233–239.
2375:
2330:(1): 299–324.
2310:
2236:
2176:
2108:
2071:(23): 235401.
2051:
2006:(14): 146802.
1993:
1984:
1931:
1871:
1869:
1866:
1865:
1864:
1859:
1854:
1849:
1844:
1839:
1834:
1829:
1824:
1817:
1814:
1804:
1801:
1758:Brillouin zone
1747:Main article:
1744:
1743:Classification
1741:
1726:
1721:
1706:
1705:Identification
1703:
1700:
1699:
1696:
1693:
1690:
1684:
1676:
1675:
1672:
1669:
1666:
1660:
1651:
1643:
1642:
1639:
1636:
1633:
1629:
1628:
1625:
1622:
1619:
1613:
1605:
1604:
1601:
1598:
1595:
1591:
1590:
1587:
1584:
1581:
1577:
1576:
1573:
1570:
1567:
1563:
1562:
1559:
1556:
1553:
1547:
1539:
1538:
1535:
1532:
1529:
1525:
1524:
1521:
1518:
1515:
1511:
1510:
1503:
1494:
1487:
1480:
1471:
1464:
1457:
1448:
1441:
1425:
1416:
1404:
1395:
1383:
1374:
1360:
1351:
1338:
1329:
1316:
1307:
1297:
1293:
1289:
1282:
1273:
1261:
1252:
1236:
1227:
1212:
1208:
1204:
1199:
1195:
1186:
1177:
1165:
1156:
1144:
1135:
1122:
1119:
1111:
1102:
1090:
1081:
1071:
1068:
1059:
1050:
1041:
1013:
1004:
915:
912:
903:
899:
895:
891:
887:
883:
875:
872:
868:optoelectronic
826:
821:
798:
764:
759:
748:with emergent
729:
724:
699:
694:
670:
665:
641:
636:
612:
607:
580:
577:
567:
564:
522:axion particle
510:
506:
502:
447:
443:
431:
427:
414:
410:
393:
390:
359:
354:
333:Eugene J. Mele
300:
297:
257:
234:
229:
174:band structure
120:band structure
97:
92:
70:
69:
31:
29:
22:
15:
9:
6:
4:
3:
2:
7811:
7800:
7797:
7795:
7792:
7791:
7789:
7774:
7773:
7764:
7762:
7761:
7756:
7752:
7750:
7749:
7740:
7738:
7737:
7728:
7727:
7724:
7718:
7715:
7713:
7710:
7708:
7705:
7703:
7700:
7698:
7695:
7694:
7692:
7690:
7686:
7680:
7677:
7673:
7670:
7668:
7665:
7664:
7663:
7660:
7658:
7655:
7653:
7650:
7648:
7645:
7643:
7640:
7638:
7635:
7633:
7630:
7628:
7625:
7623:
7620:
7619:
7617:
7615:
7611:
7605:
7602:
7600:
7597:
7595:
7592:
7590:
7587:
7585:
7582:
7580:
7577:
7575:
7572:
7570:
7567:
7565:
7562:
7561:
7559:
7555:
7545:
7542:
7540:
7537:
7535:
7532:
7530:
7527:
7525:
7522:
7521:
7519:
7515:
7509:
7506:
7504:
7501:
7499:
7496:
7494:
7491:
7489:
7486:
7484:
7483:Semiconductor
7481:
7479:
7476:
7474:
7471:
7470:
7468:
7464:
7458:
7455:
7453:
7452:Hubbard model
7450:
7448:
7445:
7443:
7440:
7438:
7435:
7433:
7430:
7428:
7425:
7423:
7420:
7418:
7415:
7413:
7410:
7408:
7405:
7404:
7402:
7398:
7392:
7389:
7387:
7384:
7382:
7379:
7377:
7374:
7372:
7369:
7367:
7364:
7362:
7359:
7357:
7354:
7353:
7351:
7347:
7344:
7340:
7334:
7331:
7329:
7326:
7324:
7321:
7319:
7316:
7315:
7313:
7309:
7304:
7294:
7291:
7289:
7286:
7284:
7281:
7279:
7276:
7274:
7271:
7269:
7266:
7264:
7261:
7259:
7256:
7254:
7251:
7249:
7246:
7244:
7241:
7240:
7238:
7236:
7232:
7228:
7221:
7216:
7214:
7209:
7207:
7202:
7201:
7198:
7190:
7186:
7182:
7178:
7174:
7169:
7164:
7159:
7154:
7150:
7146:
7142:
7137:
7133:
7132:IEEE Spectrum
7129:
7124:
7120:
7119:
7114:
7109:
7105:
7101:
7096:
7091:
7087:
7083:
7079:
7074:
7070:
7068:9783527681594
7064:
7060:
7056:
7052:
7046:
7042:
7038:
7034:
7030:
7026:
7022:
7021:
7020:Physics World
7013:
7008:
7004:
7000:
6996:
6992:
6988:
6984:
6979:
6974:
6970:
6966:
6965:
6959:
6958:
6946:
6942:
6938:
6934:
6930:
6926:
6921:
6916:
6912:
6908:
6901:
6887:
6883:
6877:
6868:
6863:
6859:
6855:
6851:
6844:
6842:
6834:
6829:
6823:
6819:
6814:
6809:
6805:
6801:
6797:
6793:
6789:
6782:
6774:
6770:
6766:
6762:
6758:
6754:
6750:
6746:
6741:
6736:
6732:
6728:
6679:
6671:
6667:
6662:
6657:
6653:
6649:
6644:
6639:
6635:
6631:
6627:
6599:
6591:
6587:
6583:
6579:
6575:
6571:
6566:
6561:
6558:(5): 053114.
6557:
6553:
6525:
6517:
6513:
6509:
6505:
6501:
6497:
6493:
6489:
6484:
6479:
6475:
6471:
6442:
6434:
6430:
6426:
6422:
6417:
6412:
6408:
6404:
6400:
6396:
6392:
6385:
6383:
6367:
6363:
6357:
6355:
6353:
6344:
6340:
6336:
6332:
6328:
6324:
6321:(10): 17049.
6320:
6316:
6309:
6307:
6305:
6296:
6292:
6288:
6284:
6280:
6276:
6272:
6268:
6263:
6258:
6254:
6250:
6243:
6241:
6232:
6228:
6224:
6220:
6216:
6212:
6208:
6204:
6200:
6196:
6191:
6186:
6182:
6178:
6150:
6142:
6138:
6134:
6130:
6126:
6122:
6118:
6114:
6107:
6099:
6095:
6091:
6087:
6083:
6079:
6075:
6071:
6022:
6014:
6008:
6000:
5996:
5992:
5988:
5984:
5980:
5976:
5972:
5967:
5962:
5958:
5954:
5946:
5938:
5934:
5930:
5926:
5922:
5918:
5914:
5910:
5906:
5902:
5897:
5892:
5889:(9): 4711–4.
5888:
5884:
5856:
5843:
5839:
5835:
5834:
5826:
5818:
5814:
5810:
5806:
5802:
5798:
5794:
5787:
5779:
5775:
5770:
5765:
5761:
5757:
5753:
5749:
5745:
5741:
5737:
5730:
5722:
5718:
5713:
5708:
5704:
5700:
5696:
5692:
5688:
5684:
5680:
5676:
5672:
5665:
5657:
5653:
5649:
5645:
5641:
5637:
5633:
5629:
5625:
5621:
5616:
5611:
5607:
5603:
5595:
5587:
5583:
5579:
5575:
5571:
5567:
5562:
5557:
5553:
5549:
5542:
5534:
5530:
5526:
5522:
5518:
5514:
5510:
5506:
5499:
5491:
5487:
5483:
5479:
5475:
5471:
5467:
5463:
5456:
5448:
5444:
5440:
5436:
5432:
5428:
5424:
5420:
5415:
5410:
5406:
5402:
5394:
5386:
5382:
5378:
5374:
5370:
5366:
5362:
5358:
5353:
5348:
5345:(9): 094516.
5344:
5340:
5333:
5325:
5321:
5317:
5313:
5309:
5305:
5301:
5297:
5292:
5287:
5284:(9): 096407.
5283:
5279:
5275:
5268:
5260:
5256:
5251:
5246:
5242:
5238:
5233:
5228:
5224:
5220:
5216:
5209:
5207:
5205:
5196:
5192:
5188:
5184:
5180:
5176:
5172:
5168:
5163:
5158:
5155:(3): 033429.
5154:
5150:
5146:
5139:
5131:
5127:
5123:
5119:
5115:
5111:
5107:
5103:
5098:
5093:
5090:(1): 012201.
5089:
5085:
5081:
5074:
5066:
5062:
5058:
5054:
5050:
5046:
5041:
5036:
5032:
5028:
5024:
5017:
5009:
5005:
5001:
4997:
4993:
4989:
4985:
4981:
4976:
4971:
4967:
4963:
4959:
4952:
4944:
4940:
4936:
4932:
4928:
4924:
4920:
4916:
4911:
4906:
4902:
4898:
4894:
4887:
4879:
4875:
4871:
4867:
4863:
4859:
4855:
4851:
4846:
4841:
4837:
4833:
4825:
4811:
4807:
4801:
4793:
4789:
4785:
4781:
4777:
4773:
4769:
4765:
4761:
4757:
4752:
4747:
4743:
4739:
4735:
4731:
4724:
4716:
4712:
4708:
4704:
4699:
4694:
4690:
4686:
4682:
4678:
4674:
4667:
4659:
4655:
4650:
4645:
4641:
4637:
4632:
4627:
4623:
4619:
4615:
4608:
4600:
4596:
4592:
4588:
4584:
4580:
4576:
4572:
4568:
4564:
4557:
4549:
4545:
4541:
4537:
4533:
4529:
4525:
4521:
4517:
4513:
4508:
4503:
4499:
4495:
4488:
4480:
4476:
4472:
4468:
4464:
4460:
4456:
4452:
4447:
4442:
4438:
4434:
4427:
4419:
4415:
4410:
4405:
4401:
4397:
4392:
4387:
4383:
4379:
4375:
4356:
4354:
4345:
4341:
4337:
4333:
4329:
4325:
4320:
4315:
4311:
4307:
4299:
4291:
4287:
4283:
4279:
4275:
4271:
4266:
4261:
4257:
4253:
4225:
4217:
4213:
4209:
4205:
4201:
4197:
4193:
4189:
4185:
4136:
4128:
4124:
4120:
4116:
4112:
4108:
4104:
4100:
4095:
4090:
4086:
4082:
4074:
4066:
4062:
4058:
4054:
4050:
4046:
4042:
4038:
4033:
4028:
4024:
4020:
4013:
4005:
4001:
3996:
3991:
3987:
3983:
3979:
3975:
3971:
3967:
3962:
3957:
3953:
3949:
3945:
3917:
3909:
3905:
3901:
3897:
3893:
3889:
3884:
3879:
3875:
3871:
3868:(9): 1162–5.
3867:
3863:
3859:
3852:
3850:
3848:
3846:
3838:
3832:
3828:
3824:
3820:
3813:
3805:
3801:
3797:
3793:
3789:
3785:
3781:
3777:
3773:
3769:
3764:
3759:
3755:
3751:
3747:
3740:
3732:
3728:
3724:
3720:
3716:
3712:
3708:
3704:
3700:
3696:
3691:
3686:
3682:
3678:
3674:
3667:
3665:
3663:
3654:
3650:
3646:
3642:
3638:
3634:
3629:
3624:
3620:
3616:
3612:
3605:
3597:
3593:
3589:
3585:
3581:
3577:
3573:
3569:
3565:
3561:
3556:
3551:
3547:
3543:
3536:
3528:
3524:
3520:
3516:
3512:
3508:
3504:
3500:
3495:
3490:
3486:
3482:
3475:
3467:
3463:
3459:
3455:
3451:
3447:
3440:
3432:
3428:
3424:
3420:
3416:
3412:
3408:
3404:
3399:
3394:
3390:
3386:
3382:
3375:
3367:
3363:
3359:
3355:
3351:
3347:
3343:
3339:
3334:
3329:
3325:
3321:
3314:
3312:
3303:
3299:
3295:
3291:
3287:
3283:
3278:
3273:
3270:(4): 045302.
3269:
3265:
3258:
3250:
3246:
3242:
3238:
3234:
3230:
3229:
3228:Physics World
3221:
3214:
3206:
3202:
3198:
3194:
3190:
3186:
3182:
3178:
3173:
3168:
3164:
3160:
3153:
3145:
3141:
3137:
3133:
3129:
3125:
3120:
3115:
3112:(4): 045302.
3111:
3107:
3100:
3092:
3088:
3084:
3080:
3076:
3072:
3068:
3064:
3059:
3054:
3050:
3046:
3039:
3031:
3027:
3023:
3019:
3014:
3009:
3005:
3001:
2994:
2986:
2982:
2978:
2974:
2970:
2966:
2962:
2958:
2954:
2950:
2945:
2940:
2936:
2932:
2928:
2921:
2913:
2909:
2905:
2901:
2897:
2893:
2889:
2885:
2880:
2875:
2871:
2867:
2863:
2856:
2848:
2844:
2840:
2836:
2832:
2828:
2824:
2820:
2815:
2810:
2806:
2802:
2798:
2791:
2783:
2779:
2775:
2771:
2767:
2763:
2759:
2755:
2750:
2745:
2741:
2737:
2733:
2726:
2718:
2714:
2710:
2706:
2702:
2698:
2694:
2690:
2686:
2682:
2677:
2672:
2668:
2664:
2660:
2653:
2651:
2649:
2640:
2636:
2632:
2628:
2624:
2620:
2616:
2612:
2608:
2601:
2599:
2591:(4): 178–181.
2590:
2586:
2582:
2575:
2573:
2564:
2560:
2556:
2552:
2548:
2544:
2540:
2536:
2531:
2526:
2522:
2518:
2514:
2507:
2499:
2495:
2491:
2487:
2483:
2479:
2475:
2471:
2467:
2463:
2459:
2452:
2444:
2440:
2436:
2432:
2428:
2424:
2420:
2416:
2412:
2408:
2403:
2398:
2394:
2390:
2386:
2379:
2371:
2367:
2363:
2359:
2355:
2351:
2347:
2343:
2338:
2333:
2329:
2325:
2321:
2314:
2306:
2302:
2298:
2294:
2290:
2286:
2282:
2278:
2273:
2268:
2264:
2260:
2256:
2249:
2247:
2245:
2243:
2241:
2232:
2228:
2224:
2220:
2216:
2212:
2207:
2202:
2198:
2194:
2190:
2183:
2181:
2172:
2168:
2164:
2160:
2156:
2152:
2148:
2144:
2139:
2134:
2130:
2126:
2122:
2115:
2113:
2104:
2100:
2095:
2090:
2086:
2082:
2078:
2074:
2070:
2066:
2062:
2055:
2047:
2043:
2039:
2035:
2031:
2027:
2023:
2019:
2014:
2009:
2005:
2001:
2000:
1988:
1980:
1976:
1972:
1968:
1964:
1960:
1955:
1950:
1946:
1942:
1935:
1927:
1923:
1919:
1915:
1911:
1907:
1903:
1899:
1895:
1891:
1887:
1883:
1876:
1872:
1863:
1860:
1858:
1855:
1853:
1850:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1819:
1813:
1811:
1800:
1798:
1794:
1793:anti-commutes
1790:
1786:
1781:
1776:
1773:
1768:
1766:
1765:vector bundle
1761:
1759:
1755:
1750:
1740:
1724:
1697:
1694:
1691:
1678:
1677:
1673:
1670:
1667:
1645:
1644:
1640:
1637:
1634:
1631:
1630:
1626:
1623:
1620:
1607:
1606:
1602:
1599:
1596:
1593:
1592:
1588:
1585:
1582:
1579:
1578:
1574:
1571:
1568:
1565:
1564:
1560:
1557:
1554:
1541:
1540:
1536:
1533:
1530:
1527:
1526:
1522:
1519:
1516:
1513:
1512:
1488:
1465:
1442:
1439:
1438:
1432:
1410:) or p-type (
1365:
1321:
1244:
1241:
1219:
1202:
1128:
1118:
1067:
1064:
1033:
1029:
1025:
1023:
1018:
995:
993:
988:
984:
979:
977:
973:
969:
965:
961:
956:
955:
951:
949:
945:
936:
932:
931:
927:
923:
921:
911:
909:
881:
871:
869:
865:
861:
857:
854:based on the
853:
849:
844:
842:
824:
787:
783:
779:
762:
747:
743:
727:
697:
668:
639:
610:
595:
591:
586:
576:
574:
563:
561:
557:
553:
548:
546:
542:
537:
535:
531:
527:
523:
519:
514:
499:
497:
493:
488:
484:
481:(ARPES). and
480:
476:
472:
468:
464:
459:
457:
453:
441:
437:
436:surface state
425:
421:
417:
405:
403:
399:
389:
387:
383:
378:
374:
357:
343:in 2006. The
342:
338:
334:
330:
325:
323:
319:
315:
311:
307:
296:
294:
290:
286:
281:
279:
275:
270:
232:
217:
213:
209:
208:U(1) symmetry
205:
201:
196:
194:
190:
186:
185:phase diagram
182:
181:adiabatically
177:
175:
170:
168:
164:
160:
156:
152:
148:
143:
141:
137:
133:
125:
121:
118:An idealized
116:
95:
78:
74:
66:
63:
55:
52:for details.
51:
46:
44:
40:
37:
32:This article
30:
26:
21:
20:
7770:
7758:
7746:
7734:
7652:Pines' demon
7502:
7391:Kondo effect
7293:Time crystal
7188:
7148:
7144:
7131:
7116:
7085:
7081:
7050:
7027:(2): 32–36.
7024:
7018:
6968:
6962:
6910:
6906:
6900:
6889:. Retrieved
6885:
6876:
6857:
6853:
6795:
6791:
6781:
6730:
6727:Nano Letters
6726:
6678:
6633:
6629:
6598:
6555:
6551:
6524:
6476:(1): 224–9.
6473:
6469:
6441:
6398:
6394:
6370:. Retrieved
6368:. 2015-06-29
6365:
6318:
6314:
6252:
6248:
6180:
6176:
6149:
6116:
6112:
6106:
6073:
6069:
6021:
6007:cite journal
5956:
5953:Nano Letters
5952:
5945:
5886:
5883:Nano Letters
5882:
5855:
5845:, retrieved
5832:
5825:
5800:
5796:
5786:
5743:
5739:
5729:
5678:
5674:
5664:
5605:
5601:
5594:
5551:
5547:
5541:
5508:
5505:Phys. Rev. B
5504:
5498:
5465:
5461:
5455:
5404:
5400:
5393:
5342:
5338:
5332:
5281:
5277:
5267:
5222:
5218:
5152:
5148:
5138:
5087:
5083:
5073:
5030:
5026:
5016:
4965:
4961:
4951:
4900:
4896:
4886:
4835:
4831:
4824:
4813:. Retrieved
4810:Science News
4809:
4800:
4741:
4737:
4723:
4680:
4676:
4666:
4621:
4617:
4607:
4566:
4562:
4556:
4497:
4493:
4487:
4436:
4432:
4426:
4381:
4377:
4362:"Sn-doped Bi
4309:
4305:
4298:
4258:(5): 57006.
4255:
4251:
4224:
4191:
4187:
4135:
4087:(7): 546–9.
4084:
4080:
4073:
4025:(7): 541–5.
4022:
4018:
4012:
3954:(1): 27483.
3951:
3947:
3916:
3865:
3861:
3818:
3812:
3753:
3749:
3739:
3680:
3676:
3618:
3614:
3604:
3545:
3541:
3535:
3484:
3480:
3474:
3449:
3445:
3439:
3391:(9): 970–4.
3388:
3384:
3374:
3326:(1): 55–78.
3323:
3319:
3267:
3263:
3257:
3235:(2): 32–36.
3232:
3226:
3213:
3162:
3158:
3152:
3109:
3105:
3099:
3048:
3044:
3038:
3003:
2999:
2993:
2934:
2930:
2920:
2869:
2865:
2855:
2804:
2800:
2790:
2739:
2735:
2725:
2666:
2662:
2617:(2): 93–96.
2614:
2610:
2588:
2585:JETP Letters
2584:
2520:
2516:
2506:
2465:
2461:
2451:
2392:
2388:
2378:
2327:
2323:
2313:
2265:(1): 22–30.
2262:
2258:
2196:
2192:
2128:
2124:
2094:10754/315777
2068:
2064:
2054:
2003:
1997:
1987:
1944:
1940:
1934:
1885:
1881:
1875:
1806:
1777:
1769:
1762:
1752:
1708:
1245:
1127:chalcogenide
1124:
1073:
1026:
996:
980:
957:
953:
952:
941:
924:
917:
882:, such as Bi
877:
845:
782:ten-fold way
781:
778:gauge theory
582:
569:
549:
538:
515:
500:
460:
406:
395:
379:
375:
326:
302:
282:
271:
197:
178:
171:
159:continuously
153:between the
144:
131:
129:
73:
58:
53:
33:
7689:Soft matter
7589:Ferromagnet
7407:Drude model
7376:Berry phase
7356:Hall effect
6913:: 145–149.
6860:(11): 154.
1789:Hamiltonian
1034:(0001) and
964:high vacuum
848:transistors
124:Fermi level
7788:Categories
7604:Spin glass
7599:Metamagnet
7579:Paramagnet
7466:Conduction
7442:BCS theory
7283:Superfluid
7278:Supersolid
6891:2022-10-11
6372:2018-07-29
5966:1601.06541
5847:2024-01-07
5615:1605.08829
5561:1505.03535
5232:2101.11412
5097:2005.08720
4815:2014-07-23
4631:1603.04317
4391:1508.03655
3961:1512.01442
3165:(9): 356.
3006:: 195322.
2530:1512.03273
1868:References
1440:Substrate
299:Prediction
200:symmetries
151:energy gap
7662:Polariton
7569:Diamagnet
7517:Couplings
7493:Conductor
7488:Semimetal
7473:Insulator
7349:Phenomena
7273:Fermi gas
6978:1002.3895
6937:0927-0256
6920:1210.5816
6822:220295733
6798:(1): 38.
6740:1004.1767
6670:0003-6951
6643:1012.1918
6590:0003-6951
6565:0906.5306
6516:118512981
6508:0040-6090
6483:1104.3438
6425:1862-6254
6366:Wiley.com
6343:2058-8437
6295:205234832
6279:0028-0836
6262:1307.6718
6215:2040-3364
6190:1308.3817
6177:Nanoscale
6141:0022-0248
6098:0022-0248
5999:206738534
5921:1530-6984
5896:1108.4978
5817:2199-160X
5703:2375-2548
5640:0036-8075
5586:119294876
5447:118353248
5414:0902.2617
5377:1098-0121
5352:1201.2176
5291:0707.1692
5259:246635019
5187:1050-2947
5162:1003.1729
5130:218674364
5122:2469-9926
5040:0901.2686
5000:1862-6254
4975:1211.5623
4935:0031-9015
4910:1304.5693
4878:205239604
4845:1402.1124
4792:119270507
4776:0031-9007
4751:0912.3750
4707:0028-0836
4591:0031-9007
4532:0031-9007
4507:0810.2998
4479:117659977
4471:1098-0121
4446:0802.3537
4384:: 11456.
4319:1409.3778
4265:0803.0052
4119:1476-1122
4094:1003.0155
4081:Nat Mater
4032:1003.0193
3986:2045-2322
3892:0935-9648
3804:118353248
3788:0036-8075
3763:0902.2617
3715:1476-4687
3690:1001.1590
3628:1002.3895
3580:0036-8075
3555:0802.1993
3398:0902.1356
3358:1947-5454
3333:1011.5462
3197:1367-2630
3172:0710.0930
3030:119407081
2969:0036-8075
2701:0036-8075
2676:0710.0582
2639:0038-1098
2563:119255437
2555:1745-2473
2490:2522-5820
2427:1476-4660
2402:1204.5700
2362:1947-5454
2337:1405.4015
2297:0094-243X
2272:0901.2686
2206:1002.3895
2171:118373714
2163:0034-6861
2138:1008.2026
2103:1098-0121
1954:1011.5462
1947:: 55–78.
1910:0028-0836
1514:graphene
922:(MOCVD),
914:Synthesis
870:devices.
420:semimetal
404:in 2007.
247: or
50:talk page
39:syntheses
7736:Category
7717:Colloids
7177:27625422
7104:20631773
7003:16066223
6945:53506226
6854:Crystals
6773:37687875
6765:20486680
6433:97544002
6287:23887427
6231:36212915
6223:24056725
5991:28337910
5937:28030427
5929:22827514
5778:28516906
5721:27051869
5656:29455044
5648:23493424
5490:10043303
5439:19213915
5385:59462024
5316:18352737
5195:21800060
5065:14320124
5008:52082807
4943:55912821
4870:25056062
4784:20366446
4715:23235853
4658:27934759
4599:10034541
4540:19392469
4418:27118032
4344:51843826
4216:19905585
4127:20512153
4065:32178219
4057:20512154
4004:27270569
3908:33855507
3900:21360770
3796:19213915
3723:19620959
3653:16066223
3596:15306515
3588:17702909
3519:16384250
3423:18432240
3366:11516573
3302:15011491
3205:13999448
3144:15011491
3083:17358555
2977:17170299
2904:16241681
2839:16605772
2774:16384250
2709:17885096
2498:53694955
2443:39748656
2435:23241532
2370:12669555
2305:14320124
2231:16066223
2038:16241681
1979:11516573
1918:20220837
1816:See also
1509: %
1486: %
1463: %
463:antimony
293:acoustic
289:magnetic
285:photonic
7748:Commons
7712:Polymer
7679:Polaron
7657:Plasmon
7637:Exciton
7191:. 2017.
7168:5027448
7029:Bibcode
6983:Bibcode
6800:Bibcode
6745:Bibcode
6648:Bibcode
6570:Bibcode
6488:Bibcode
6403:Bibcode
6323:Bibcode
6195:Bibcode
6121:Bibcode
6078:Bibcode
5971:Bibcode
5901:Bibcode
5769:5454374
5748:Bibcode
5712:4820380
5683:Bibcode
5620:Bibcode
5602:Science
5566:Bibcode
5533:9999836
5513:Bibcode
5470:Bibcode
5419:Bibcode
5401:Science
5357:Bibcode
5324:7618062
5296:Bibcode
5237:Bibcode
5225:: 664.
5219:Quantum
5167:Bibcode
5102:Bibcode
5045:Bibcode
4980:Bibcode
4915:Bibcode
4850:Bibcode
4756:Bibcode
4685:Bibcode
4636:Bibcode
4618:Science
4571:Bibcode
4548:1133717
4512:Bibcode
4451:Bibcode
4409:4853473
4324:Bibcode
4290:9282408
4270:Bibcode
4196:Bibcode
4099:Bibcode
4037:Bibcode
3995:4895388
3966:Bibcode
3870:Bibcode
3768:Bibcode
3750:Science
3731:4369601
3695:Bibcode
3633:Bibcode
3560:Bibcode
3542:Science
3527:6080059
3499:Bibcode
3454:Bibcode
3431:4402113
3403:Bibcode
3338:Bibcode
3282:Bibcode
3237:Bibcode
3177:Bibcode
3124:Bibcode
3091:6037351
3063:Bibcode
2985:7295726
2949:Bibcode
2931:Science
2912:1775498
2884:Bibcode
2847:2618285
2819:Bibcode
2782:6080059
2754:Bibcode
2717:8836690
2681:Bibcode
2663:Science
2619:Bibcode
2535:Bibcode
2470:Bibcode
2407:Bibcode
2342:Bibcode
2277:Bibcode
2211:Bibcode
2143:Bibcode
2073:Bibcode
2046:1775498
2018:Bibcode
1959:Bibcode
1926:1911343
1890:Bibcode
1780:unitary
1030:(111),
1024:(111),
987:defects
972:sublime
960:epitaxy
573:Floquet
440:Kramers
382:bismuth
147:trivial
7647:Phonon
7642:Magnon
7400:Theory
7258:Plasma
7248:Liquid
7175:
7165:
7102:
7082:Nature
7065:
7001:
6943:
6935:
6820:
6771:
6763:
6668:
6588:
6514:
6506:
6431:
6423:
6341:
6293:
6285:
6277:
6249:Nature
6229:
6221:
6213:
6139:
6096:
5997:
5989:
5935:
5927:
5919:
5815:
5776:
5766:
5719:
5709:
5701:
5654:
5646:
5638:
5584:
5531:
5488:
5445:
5437:
5383:
5375:
5322:
5314:
5257:
5193:
5185:
5128:
5120:
5063:
5006:
4998:
4941:
4933:
4876:
4868:
4832:Nature
4790:
4782:
4774:
4713:
4705:
4677:Nature
4656:
4597:
4589:
4546:
4538:
4530:
4477:
4469:
4416:
4406:
4342:
4288:
4214:
4125:
4117:
4063:
4055:
4002:
3992:
3984:
3906:
3898:
3890:
3833:
3802:
3794:
3786:
3729:
3721:
3713:
3677:Nature
3651:
3594:
3586:
3578:
3525:
3517:
3429:
3421:
3385:Nature
3364:
3356:
3300:
3203:
3195:
3142:
3089:
3081:
3028:
2983:
2975:
2967:
2910:
2902:
2845:
2837:
2780:
2772:
2715:
2707:
2699:
2637:
2561:
2553:
2496:
2488:
2441:
2433:
2425:
2368:
2360:
2303:
2295:
2229:
2169:
2161:
2101:
2044:
2036:
1977:
1924:
1916:
1908:
1882:Nature
1558:-11.9
1534:-12.3
1523:-42.3
1520:-43.8
1517:-40.6
532:using
492:doping
477:using
291:, and
167:vacuum
163:border
36:biased
7622:Anyon
7243:Solid
7015:(PDF)
6999:S2CID
6973:arXiv
6941:S2CID
6915:arXiv
6818:S2CID
6769:S2CID
6735:arXiv
6638:arXiv
6560:arXiv
6512:S2CID
6478:arXiv
6429:S2CID
6291:S2CID
6257:arXiv
6227:S2CID
6185:arXiv
5995:S2CID
5961:arXiv
5933:S2CID
5891:arXiv
5803:(6).
5652:S2CID
5610:arXiv
5582:S2CID
5556:arXiv
5443:S2CID
5409:arXiv
5381:S2CID
5347:arXiv
5320:S2CID
5286:arXiv
5255:S2CID
5227:arXiv
5191:S2CID
5157:arXiv
5126:S2CID
5092:arXiv
5061:S2CID
5035:arXiv
5004:S2CID
4970:arXiv
4939:S2CID
4905:arXiv
4874:S2CID
4840:arXiv
4788:S2CID
4746:arXiv
4626:arXiv
4544:S2CID
4502:arXiv
4475:S2CID
4441:arXiv
4386:arXiv
4340:S2CID
4314:arXiv
4286:S2CID
4260:arXiv
4089:arXiv
4061:S2CID
4027:arXiv
3956:arXiv
3904:S2CID
3800:S2CID
3758:arXiv
3727:S2CID
3685:arXiv
3649:S2CID
3623:arXiv
3592:S2CID
3550:arXiv
3523:S2CID
3489:arXiv
3427:S2CID
3393:arXiv
3362:S2CID
3328:arXiv
3298:S2CID
3272:arXiv
3223:(PDF)
3201:S2CID
3167:arXiv
3140:S2CID
3114:arXiv
3087:S2CID
3053:arXiv
3026:S2CID
3008:arXiv
2981:S2CID
2939:arXiv
2908:S2CID
2874:arXiv
2843:S2CID
2809:arXiv
2778:S2CID
2744:arXiv
2713:S2CID
2671:arXiv
2559:S2CID
2525:arXiv
2494:S2CID
2439:S2CID
2397:arXiv
2366:S2CID
2332:arXiv
2301:S2CID
2267:arXiv
2227:S2CID
2201:arXiv
2167:S2CID
2133:arXiv
2042:S2CID
2008:arXiv
1975:S2CID
1949:arXiv
1922:S2CID
1698:15.5
1695:12.1
1692:18.6
1674:12.0
1668:14.9
1635:10.7
1632:CdTe
1603:-2.3
1600:-5.3
1589:-2.8
1586:-5.7
1583:-0.2
1575:-5.9
1572:-8.7
1569:-3.4
1566:GaAs
1561:-9.2
1555:-6.8
1537:-9.7
1531:-7.3
1290:2 − x
1196:1 − x
541:Kondo
444:1 − x
428:1 − x
411:1 − x
7632:Hole
7173:PMID
7100:PMID
7063:ISBN
6933:ISSN
6761:PMID
6704:and
6666:ISSN
6586:ISSN
6504:ISSN
6421:ISSN
6339:ISSN
6283:PMID
6275:ISSN
6219:PMID
6211:ISSN
6137:ISSN
6094:ISSN
6013:link
5987:PMID
5925:PMID
5917:ISSN
5813:ISSN
5774:PMID
5717:PMID
5699:ISSN
5644:PMID
5636:ISSN
5529:PMID
5486:PMID
5435:PMID
5373:ISSN
5312:PMID
5183:ISSN
5118:ISSN
5031:1134
4996:ISSN
4931:ISSN
4866:PMID
4780:PMID
4772:ISSN
4711:PMID
4703:ISSN
4654:PMID
4595:PMID
4587:ISSN
4536:PMID
4528:ISSN
4467:ISSN
4414:PMID
4212:PMID
4163:and
4123:PMID
4115:ISSN
4053:PMID
4000:PMID
3982:ISSN
3896:PMID
3888:ISSN
3831:ISBN
3792:PMID
3784:ISSN
3719:PMID
3711:ISSN
3584:PMID
3576:ISSN
3515:PMID
3419:PMID
3354:ISSN
3193:ISSN
3079:PMID
2973:PMID
2965:ISSN
2900:PMID
2835:PMID
2770:PMID
2705:PMID
2697:ISSN
2635:ISSN
2551:ISSN
2486:ISSN
2431:PMID
2423:ISSN
2358:ISSN
2293:ISSN
2263:1134
2159:ISSN
2099:ISSN
2034:PMID
1914:PMID
1906:ISSN
1671:8.7
1641:7.8
1638:4.6
1627:2.8
1624:0.1
1621:5.9
1597:0.2
1594:InP
1580:CdS
1203:, Bi
1022:GaAs
985:and
946:and
866:and
858:and
850:for
528:and
473:and
398:HgTe
339:and
331:and
318:CdTe
314:HgTe
312:and
310:SnTe
306:PbTe
274:spin
7253:Gas
7163:PMC
7153:doi
7149:113
7090:doi
7086:466
7055:doi
7037:doi
6991:doi
6925:doi
6862:doi
6808:doi
6753:doi
6656:doi
6578:doi
6550:".
6496:doi
6474:520
6411:doi
6331:doi
6267:doi
6253:499
6203:doi
6129:doi
6117:271
6086:doi
6074:253
5979:doi
5909:doi
5838:doi
5805:doi
5764:PMC
5756:doi
5707:PMC
5691:doi
5628:doi
5606:340
5574:doi
5521:doi
5478:doi
5427:doi
5405:323
5365:doi
5304:doi
5282:100
5245:doi
5175:doi
5110:doi
5088:103
5053:doi
4988:doi
4923:doi
4858:doi
4836:511
4764:doi
4742:104
4693:doi
4681:492
4644:doi
4622:354
4579:doi
4520:doi
4498:102
4459:doi
4404:PMC
4396:doi
4368:0.9
4364:1.1
4332:doi
4278:doi
4252:EPL
4204:doi
4192:103
4107:doi
4045:doi
3990:PMC
3974:doi
3878:doi
3823:doi
3776:doi
3754:323
3703:doi
3681:460
3641:doi
3568:doi
3546:317
3507:doi
3462:doi
3411:doi
3389:452
3346:doi
3290:doi
3245:doi
3185:doi
3132:doi
3071:doi
3018:doi
2957:doi
2935:314
2892:doi
2827:doi
2762:doi
2689:doi
2667:318
2627:doi
2543:doi
2478:doi
2415:doi
2350:doi
2285:doi
2219:doi
2151:doi
2089:hdl
2081:doi
2026:doi
1967:doi
1898:doi
1886:464
1680:SiO
1609:BaF
1543:CaF
1528:Si
1209:0.9
1205:1.1
1192:or
1032:CdS
1028:InP
966:or
562:).
507:0.9
503:1.1
413:Sb
41:of
7790::
7187:.
7171:.
7161:.
7147:.
7143:.
7130:.
7115:.
7098:.
7080:.
7061:.
7035:.
7025:24
7023:.
7017:.
6997:.
6989:.
6981:.
6969:82
6967:.
6939:.
6931:.
6923:.
6911:70
6909:.
6884:.
6856:.
6852:.
6840:^
6816:.
6806:.
6794:.
6790:.
6767:.
6759:.
6751:.
6743:.
6731:10
6729:.
6715:Te
6706:Bi
6694:Se
6685:Bi
6664:.
6654:.
6646:.
6634:97
6632:.
6628:.
6616:Se
6607:Bi
6584:.
6576:.
6568:.
6556:95
6554:.
6540:Se
6531:Bi
6510:.
6502:.
6494:.
6486:.
6472:.
6458:Se
6449:Bi
6427:.
6419:.
6409:.
6397:.
6393:.
6381:^
6364:.
6351:^
6337:.
6329:.
6317:.
6303:^
6289:.
6281:.
6273:.
6265:.
6251:.
6239:^
6225:.
6217:.
6209:.
6201:.
6193:.
6179:.
6165:Se
6156:Bi
6135:.
6127:.
6115:.
6092:.
6084:.
6072:.
6058:Se
6049:Bi
6037:Se
6028:Sb
6009:}}
6005:{{
5993:.
5985:.
5977:.
5969:.
5957:17
5955:.
5931:.
5923:.
5915:.
5907:.
5899:.
5887:12
5885:.
5871:Se
5862:Bi
5836:,
5811:.
5799:.
5795:.
5772:.
5762:.
5754:.
5742:.
5738:.
5715:.
5705:.
5697:.
5689:.
5677:.
5673:.
5650:.
5642:.
5634:.
5626:.
5618:.
5604:.
5580:.
5572:.
5564:.
5552:88
5550:.
5527:.
5519:.
5509:44
5507:.
5484:.
5476:.
5466:66
5464:.
5441:.
5433:.
5425:.
5417:.
5403:.
5379:.
5371:.
5363:.
5355:.
5343:85
5341:.
5318:.
5310:.
5302:.
5294:.
5280:.
5276:.
5253:.
5243:.
5235:.
5221:.
5217:.
5203:^
5189:.
5181:.
5173:.
5165:.
5153:82
5151:.
5147:.
5124:.
5116:.
5108:.
5100:.
5086:.
5082:.
5059:.
5051:.
5043:.
5029:.
5025:.
5002:.
4994:.
4986:.
4978:.
4964:.
4960:.
4937:.
4929:.
4921:.
4913:.
4901:82
4899:.
4895:.
4872:.
4864:.
4856:.
4848:.
4834:.
4808:.
4786:.
4778:.
4770:.
4762:.
4754:.
4740:.
4732:;
4709:.
4701:.
4691:.
4679:.
4675:.
4652:.
4642:.
4634:.
4620:.
4616:.
4593:.
4585:.
4577:.
4567:58
4565:.
4542:.
4534:.
4526:.
4518:.
4510:.
4496:.
4473:.
4465:.
4457:.
4449:.
4437:78
4435:.
4412:.
4402:.
4394:.
4380:.
4376:.
4370:Te
4366:Sb
4352:^
4338:.
4330:.
4322:.
4310:10
4308:.
4284:.
4276:.
4268:.
4256:81
4254:.
4240:Te
4231:Bi
4210:.
4202:.
4190:.
4186:.
4174:Te
4165:Sb
4153:Te
4144:Bi
4121:.
4113:.
4105:.
4097:.
4083:.
4059:.
4051:.
4043:.
4035:.
4021:.
3998:.
3988:.
3980:.
3972:.
3964:.
3950:.
3946:.
3934:Se
3925:Bi
3902:.
3894:.
3886:.
3876:.
3866:23
3864:.
3860:.
3844:^
3829:,
3798:.
3790:.
3782:.
3774:.
3766:.
3752:.
3748:.
3725:.
3717:.
3709:.
3701:.
3693:.
3679:.
3675:.
3661:^
3647:.
3639:.
3631:.
3619:82
3617:.
3613:.
3590:.
3582:.
3574:.
3566:.
3558:.
3544:.
3521:.
3513:.
3505:.
3497:.
3485:95
3483:.
3460:.
3448:.
3425:.
3417:.
3409:.
3401:.
3387:.
3360:.
3352:.
3344:.
3336:.
3322:.
3310:^
3296:.
3288:.
3280:.
3268:76
3266:.
3243:.
3233:24
3231:.
3225:.
3199:.
3191:.
3183:.
3175:.
3161:.
3138:.
3130:.
3122:.
3110:76
3108:.
3085:.
3077:.
3069:.
3061:.
3049:98
3047:.
3024:.
3016:.
3004:79
3002:.
2979:.
2971:.
2963:.
2955:.
2947:.
2933:.
2929:.
2906:.
2898:.
2890:.
2882:.
2870:95
2868:.
2864:.
2841:.
2833:.
2825:.
2817:.
2805:96
2803:.
2799:.
2776:.
2768:.
2760:.
2752:.
2740:95
2738:.
2734:.
2711:.
2703:.
2695:.
2687:.
2679:.
2665:.
2661:.
2647:^
2633:.
2625:.
2615:61
2613:.
2609:.
2597:^
2589:42
2587:.
2583:.
2571:^
2557:.
2549:.
2541:.
2533:.
2521:12
2519:.
2515:.
2492:.
2484:.
2476:.
2464:.
2460:.
2437:.
2429:.
2421:.
2413:.
2405:.
2393:12
2391:.
2387:.
2364:.
2356:.
2348:.
2340:.
2326:.
2322:.
2299:.
2291:.
2283:.
2275:.
2261:.
2257:.
2239:^
2225:.
2217:.
2209:.
2197:82
2195:.
2191:.
2179:^
2165:.
2157:.
2149:.
2141:.
2129:83
2127:.
2123:.
2111:^
2097:.
2087:.
2079:.
2069:85
2067:.
2063:.
2040:.
2032:.
2024:.
2016:.
2004:95
2002:.
1973:.
1965:.
1957:.
1943:.
1920:.
1912:.
1904:.
1896:.
1884:.
1799:.
1760:.
1647:Al
1499:Te
1490:Sb
1476:Te
1467:Bi
1453:Se
1444:Bi
1421:Te
1412:Sb
1400:Te
1391:Bi
1389:,
1379:Se
1370:Bi
1356:Te
1347:Sb
1344:,
1334:Te
1325:Bi
1323:,
1312:Se
1303:Bi
1296:Se
1292:In
1278:Se
1269:Bi
1257:Te
1248:Bi
1232:Te
1223:Bi
1211:Te
1207:Sb
1198:Sb
1194:Bi
1182:Te
1173:Sb
1171:,
1161:Te
1152:Bi
1150:,
1140:Se
1131:Bi
1107:Te
1098:Bi
1096:,
1086:Se
1077:Bi
1066:.
1060:12
1046:Fe
1020:,
1000:Al
978:.
950:.
902:Te
894:Se
886:Te
843:.
810:,
509:Te
505:Sb
469:,
465:,
446:Sb
430:Sb
409:Bi
388:.
287:,
130:A
7219:e
7212:t
7205:v
7179:.
7155::
7134:.
7121:.
7106:.
7092::
7071:.
7057::
7043:.
7039::
7031::
7005:.
6993::
6985::
6975::
6947:.
6927::
6917::
6894:.
6870:.
6864::
6858:6
6835:.
6824:.
6810::
6802::
6796:1
6775:.
6755::
6747::
6737::
6720:3
6711:2
6699:3
6690:2
6672:.
6658::
6650::
6640::
6621:3
6612:2
6592:.
6580::
6572::
6562::
6545:3
6536:2
6518:.
6498::
6490::
6480::
6463:3
6454:2
6435:.
6413::
6405::
6399:7
6375:.
6345:.
6333::
6325::
6319:2
6297:.
6269::
6259::
6233:.
6205::
6197::
6187::
6181:5
6170:3
6161:2
6143:.
6131::
6123::
6100:.
6088::
6080::
6063:3
6054:2
6042:3
6033:2
6015:)
6001:.
5981::
5973::
5963::
5939:.
5911::
5903::
5893::
5876:3
5867:2
5840::
5819:.
5807::
5801:5
5780:.
5758::
5750::
5744:8
5723:.
5693::
5685::
5679:2
5658:.
5630::
5622::
5612::
5588:.
5576::
5568::
5558::
5535:.
5523::
5515::
5492:.
5480::
5472::
5449:.
5429::
5421::
5411::
5387:.
5367::
5359::
5349::
5326:.
5306::
5298::
5288::
5261:.
5247::
5239::
5229::
5223:6
5197:.
5177::
5169::
5159::
5132:.
5112::
5104::
5094::
5067:.
5055::
5047::
5037::
5010:.
4990::
4982::
4972::
4966:7
4945:.
4925::
4917::
4907::
4880:.
4860::
4852::
4842::
4818:.
4794:.
4766::
4758::
4748::
4717:.
4695::
4687::
4660:.
4646::
4638::
4628::
4601:.
4581::
4573::
4550:.
4522::
4514::
4504::
4481:.
4461::
4453::
4443::
4420:.
4398::
4388::
4382:7
4372:2
4346:.
4334::
4326::
4316::
4292:.
4280::
4272::
4262::
4245:3
4236:2
4218:.
4206::
4198::
4184:"
4179:3
4170:2
4158:3
4149:2
4129:.
4109::
4101::
4091::
4085:9
4067:.
4047::
4039::
4029::
4023:9
4006:.
3976::
3968::
3958::
3952:6
3939:3
3930:2
3910:.
3880::
3872::
3825::
3806:.
3778::
3770::
3760::
3733:.
3705::
3697::
3687::
3655:.
3643::
3635::
3625::
3598:.
3570::
3562::
3552::
3529:.
3509::
3501::
3491::
3468:.
3464::
3456::
3450:8
3433:.
3413::
3405::
3395::
3368:.
3348::
3340::
3330::
3324:2
3304:.
3292::
3284::
3274::
3251:.
3247::
3239::
3207:.
3187::
3179::
3169::
3163:9
3146:.
3134::
3126::
3116::
3093:.
3073::
3065::
3055::
3032:.
3020::
3010::
2987:.
2959::
2951::
2941::
2914:.
2894::
2886::
2876::
2849:.
2829::
2821::
2811::
2784:.
2764::
2756::
2746::
2719:.
2691::
2683::
2673::
2641:.
2629::
2621::
2565:.
2545::
2537::
2527::
2500:.
2480::
2472::
2466:1
2445:.
2417::
2409::
2399::
2372:.
2352::
2344::
2334::
2328:6
2307:.
2287::
2279::
2269::
2233:.
2221::
2213::
2203::
2173:.
2153::
2145::
2135::
2105:.
2091::
2083::
2075::
2048:.
2028::
2020::
2010::
1994:2
1981:.
1969::
1961::
1951::
1945:2
1928:.
1900::
1892::
1725:2
1720:Z
1685:2
1661:3
1656:O
1652:2
1614:2
1548:2
1504:3
1495:2
1481:3
1472:2
1458:3
1449:2
1426:3
1417:2
1405:3
1396:2
1384:3
1375:2
1361:3
1352:2
1339:3
1330:2
1317:3
1308:2
1298:3
1294:x
1283:3
1274:2
1262:3
1253:2
1237:3
1228:2
1213:2
1200:x
1187:3
1178:2
1166:3
1157:2
1145:3
1136:2
1112:3
1103:2
1091:3
1082:2
1055:O
1051:5
1042:3
1037:Y
1014:3
1009:O
1005:2
904:3
900:2
896:3
892:2
888:3
884:2
825:2
820:Z
797:Z
763:2
758:Z
728:2
723:Z
698:2
693:Z
669:2
664:Z
640:2
635:Z
611:2
606:Z
558:(
511:2
448:x
432:x
415:x
358:2
353:Z
316:/
308:/
256:Z
233:2
228:Z
96:2
91:Z
65:)
59:(
45:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.