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Energy gap

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If the density of states vanishes over an extended energy range, then this is called a hard gap. If instead the density of states exactly vanishes only for a single energy value (while being suppressed, but not vanishing for nearby energy values), then this is called a soft gap. A prototypical
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are to a large extent determined by their band gaps, but also for insulators and metals the band structure—and thus any possible band gaps—govern their electronic properties.
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of the superconducting energy gap for conventional superconductors at zero temperature scales with their critical temperature
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If the density of states is suppressed near the Fermi energy but does not fully vanish, then this suppression is called
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Timusk, Tom; Statt, Bryan (1999). "The pseudogap in high-temperature superconductors: an experimental survey".
564: 321:. Pseudogaps are experimentally observed in a variety of material classes; a prominent example are the 100:. Here, the size of the energy gap indicates the energy gain for two electrons upon formation of a 47: 283: 185: 136: 107: 51: 165: 527: 477: 8: 20: 531: 481: 493: 467: 278: 489: 438: 407: 374: 367: 40: 539: 497: 535: 515: 485: 511: 430: 362: 397: 89: 63: 518:(1975). "Coulomb gap and low temperature conductivity of disordered systems". 553: 358: 71: 93: 472: 335: 101: 162:, and it grows upon further cooling. BCS theory predicts that the size 97: 92:
the energy gap is a region of suppressed density of states around the
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that exists in localized electron states with Coulomb interaction.
67: 36: 28: 357: 133:, it starts to open upon entering the superconducting state at 32: 54:, a term which need not be specific to electrons or solids. 270:{\displaystyle \Delta (T=0)=1.764\,k_{\rm {B}}T_{\rm {c}}} 286: 217: 188: 168: 139: 110: 50:, an energy gap is often known more abstractly as a 366: 301: 269: 203: 174: 154: 125: 551: 510: 429: 396: 353: 351: 425: 423: 39:states exist, i.e. an energy range where the 16:Forbidden energy state in solid state physics 392: 390: 457: 348: 420: 471: 451: 387: 242: 504: 328: 323:cuprate high-temperature superconductors 406:(7th ed.). John Wiley & Sons. 552: 403:Introduction to Solid State Physics 13: 293: 261: 249: 218: 195: 169: 146: 117: 77: 14: 576: 435:Introduction to Superconductivity 62:If an energy gap exists in the 233: 221: 1: 437:(2nd ed.). McGraw-Hill. 341: 334:example of a soft gap is the 70:. The physical properties of 520:J. Phys. C: Solid State Phys 312: 66:of a material, it is called 7: 302:{\displaystyle k_{\rm {B}}} 204:{\displaystyle T_{\rm {c}}} 155:{\displaystyle T_{\rm {c}}} 126:{\displaystyle T_{\rm {c}}} 57: 10: 581: 560:Electronic band structures 490:10.1088/0034-4885/62/1/002 81: 540:10.1088/0022-3719/8/4/003 48:condensed matter physics 31:is an energy range in a 175:{\displaystyle \Delta } 303: 271: 205: 176: 156: 127: 329:Hard gap vs. soft gap 304: 272: 206: 177: 157: 128: 373:. Saunders College. 284: 215: 186: 166: 137: 108: 532:1975JPhC....8L..49E 482:1999RPPh...62...61T 369:Solid State Physics 84:Superconducting gap 21:solid-state physics 299: 279:Boltzmann constant 267: 201: 172: 152: 123: 565:Superconductivity 41:density of states 572: 544: 543: 516:Shklovskii, B.I. 508: 502: 501: 475: 473:cond-mat/9905219 455: 449: 448: 427: 418: 417: 394: 385: 384: 372: 359:Neil N. Ashcroft 355: 308: 306: 305: 300: 298: 297: 296: 276: 274: 273: 268: 266: 265: 264: 254: 253: 252: 210: 208: 207: 202: 200: 199: 198: 181: 179: 178: 173: 161: 159: 158: 153: 151: 150: 149: 132: 130: 129: 124: 122: 121: 120: 580: 579: 575: 574: 573: 571: 570: 569: 550: 549: 548: 547: 509: 505: 460:Rep. Prog. Phys 456: 452: 445: 431:Michael Tinkham 428: 421: 414: 395: 388: 381: 363:N. David Mermin 356: 349: 344: 331: 315: 292: 291: 287: 285: 282: 281: 260: 259: 255: 248: 247: 243: 216: 213: 212: 194: 193: 189: 187: 184: 183: 167: 164: 163: 145: 144: 140: 138: 135: 134: 116: 115: 111: 109: 106: 105: 90:superconductors 86: 80: 78:Superconductors 60: 17: 12: 11: 5: 578: 568: 567: 562: 546: 545: 526:(4): L49–L51. 503: 450: 443: 419: 412: 398:Charles Kittel 386: 379: 346: 345: 343: 340: 330: 327: 314: 311: 295: 290: 263: 258: 251: 246: 241: 238: 235: 232: 229: 226: 223: 220: 197: 192: 171: 148: 143: 119: 114: 79: 76: 72:semiconductors 64:band structure 59: 56: 46:Especially in 15: 9: 6: 4: 3: 2: 577: 566: 563: 561: 558: 557: 555: 541: 537: 533: 529: 525: 521: 517: 513: 507: 499: 495: 491: 487: 483: 479: 474: 469: 466:(1): 61–122. 465: 461: 454: 446: 444:0-07-064878-6 440: 436: 432: 426: 424: 415: 413:0-471-11181-3 409: 405: 404: 399: 393: 391: 382: 380:0-03-083993-9 376: 371: 370: 364: 360: 354: 352: 347: 339: 337: 326: 324: 320: 310: 288: 280: 256: 244: 239: 236: 230: 227: 224: 190: 141: 112: 103: 99: 95: 91: 85: 75: 73: 69: 65: 55: 53: 49: 44: 42: 38: 34: 30: 26: 22: 523: 519: 506: 463: 459: 453: 434: 401: 368: 332: 316: 94:Fermi energy 87: 61: 52:spectral gap 45: 24: 18: 512:Efros, A.L. 336:Coulomb gap 102:Cooper pair 554:Categories 342:References 98:BCS theory 82:See also: 43:vanishes. 25:energy gap 319:pseudogap 313:Pseudogap 219:Δ 170:Δ 35:where no 498:17302108 433:(1996). 400:(1996). 365:(1976). 68:band gap 58:Band gap 37:electron 29:band gap 528:Bibcode 478:Bibcode 496:  441:  410:  377:  277:(with 494:S2CID 468:arXiv 240:1.764 33:solid 23:, an 439:ISBN 408:ISBN 375:ISBN 88:For 536:doi 486:doi 309:). 27:or 19:In 556:: 534:. 522:. 514:; 492:. 484:. 476:. 464:62 462:. 422:^ 389:^ 361:; 350:^ 325:. 211:: 542:. 538:: 530:: 524:8 500:. 488:: 480:: 470:: 447:. 416:. 383:. 294:B 289:k 262:c 257:T 250:B 245:k 237:= 234:) 231:0 228:= 225:T 222:( 196:c 191:T 147:c 142:T 118:c 113:T

Index

solid-state physics
band gap
solid
electron
density of states
condensed matter physics
spectral gap
band structure
band gap
semiconductors
Superconducting gap
superconductors
Fermi energy
BCS theory
Cooper pair
Boltzmann constant
pseudogap
cuprate high-temperature superconductors
Coulomb gap


Neil N. Ashcroft
N. David Mermin
Solid State Physics
ISBN
0-03-083993-9


Charles Kittel
Introduction to Solid State Physics

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