675:, no two fermions can be in the same state. Additionally, at zero temperature the enthalpy of the electrons must be minimal, meaning that they cannot change state. If, for a particle in some state, there existed an unoccupied lower state that it could occupy, then the energy difference between those states would give the electron an additional enthalpy. Hence, the enthalpy of the electron would not be minimal. Therefore, at zero temperature all the lowest energy states must be saturated. For a large ensemble the Fermi level will be approximately equal to the chemical potential of the system, and hence every state below this energy must be occupied. Thus, particles fill up all energy levels below the Fermi level at absolute zero, which is equivalent to saying that is the energy level below which there are exactly
1619:
118:
25:
1531:
867:
1527:. Therefore, dHvA and SdH experiments are usually performed at high-field facilities like the High Field Magnet Laboratory in Netherlands, Grenoble High Magnetic Field Laboratory in France, the Tsukuba Magnet Laboratory in Japan or the National High Magnetic Field Laboratory in the United States.
1581:
it is also possible to determine the Fermi surface as the annihilation process conserves the momentum of the initial particle. Since a positron in a solid will thermalize prior to annihilation, the annihilation radiation carries the information about the electron momentum. The corresponding
666:
1522:
Thus the determination of the periods of oscillation for various applied field directions allows mapping of the Fermi surface. Observation of the dHvA and SdH oscillations requires magnetic fields large enough that the circumference of the cyclotron orbit is smaller than a
821:
292:
1602:
conditions, cryogenic temperatures, high magnetic fields or fully ordered alloys. However, ACAR needs samples with a low vacancy concentration as they act as effective traps for positrons. In this way, the first determination of a
1154:
so at finite temperatures the Fermi surface is accordingly broadened. In principle all fermion energy level populations are bound by a Fermi surface although the term is not generally used outside of condensed-matter physics.
734:
The linear response of a metal to an electric, magnetic, or thermal gradient is determined by the shape of the Fermi surface, because currents are due to changes in the occupancy of states near the Fermi energy. In
557:
1516:
1583:
122:
952:, which results in a portion of the Fermi surface lying in the second (or higher) zones. As with the band structure itself, the Fermi surface can be displayed in an extended-zone scheme where
333:
1317:
1261:
917:
1007:
382:
186:
1121:
1099:
1077:
1055:
1033:
972:
946:
729:
516:
460:
1454:
1423:
745:
845:
549:
2028:
1368:
424:
1225:
194:
93:
which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the
1392:
1341:
1181:
693:
482:
402:
353:
155:
1590:
of both annihilation quanta. In this way it is possible to probe the electron momentum density of a solid and determine the Fermi surface. Furthermore, using
1598:
states in magnetized materials can be obtained. ACAR has many advantages and disadvantages compared to other experimental techniques: It does not rely on
1642:
1567:
1563:
1822:
Weber, J. A.; Böni, P.; Ceeh, H.; Leitner, M.; Hugenschmidt, Ch (2013-01-01). "First 2D-ACAR Measurements on Cu with the new
Spectrometer at TUM".
890:
Fermi surface of graphite, which has both electron and hole pockets in its Fermi surface due to multiple bands crossing the Fermi energy along the
1618:
1896:
1371:
661:{\displaystyle \left\langle n_{i}\right\rangle \to {\begin{cases}1&(\epsilon _{i}<\mu )\\0&(\epsilon _{i}>\mu )\end{cases}}.}
2033:
46:
1227:
and occur because of the quantization of energy levels in the plane perpendicular to a magnetic field, a phenomenon first predicted by
1943:
1929:
2023:
1772:
1747:
68:
1462:
1163:
Electronic Fermi surfaces have been measured through observation of the oscillation of transport properties in magnetic fields
1184:
1647:
1558:
The most direct experimental technique to resolve the electronic structure of crystals in the momentum-energy space (see
1188:
1320:
303:
117:
1151:
158:
39:
33:
1542:. The experimental data shown as an intensity plot in yellow-red-black scale. Green dashed rectangle represents the
105:, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called
1951:
1266:
672:
102:
98:
1127:
where the condensation energy comes from opening a gap at the Fermi surface. Examples of such ground states are
1123:. Solids with a large density of states at the Fermi level become unstable at low temperatures and tend to form
50:
82:
1234:
121:
Fig. 1: Fermi surface and electron momentum density of copper in the reduced zone schema measured with
1192:
848:
1136:
1652:
1535:
1578:
856:
893:
1997:
1974:
1947:
1841:
1708:
1685:
485:
980:
587:
1933:
360:
164:
94:
1938:"Angle-resolved photoemission spectroscopy of the cuprate superconductors (Review Article)" (2002)
1104:
1082:
1060:
1038:
1016:
955:
1865:
1831:
1559:
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974:
is allowed to have arbitrarily large values or a reduced-zone scheme where wavevectors are shown
922:
816:{\displaystyle k_{\rm {F}}={\frac {p_{\rm {F}}}{\hbar }}={\frac {\sqrt {2mE_{\rm {F}}}}{\hbar }}}
736:
705:
519:
492:
436:
427:
1432:
2002:
1892:
1857:
1804:
1768:
1743:
1713:
1599:
1591:
1405:
1140:
1992:
1982:
1849:
1703:
1693:
1530:
1010:
830:
528:
90:
1346:
287:{\displaystyle \langle n_{i}\rangle ={\frac {1}{e^{(\epsilon _{i}-\mu )/k_{\rm {B}}T}+1}},}
409:
1853:
1202:
1987:
1978:
1962:
1845:
1698:
1689:
1673:
1637:
1624:
1595:
1543:
1524:
1426:
1395:
1377:
1326:
1166:
1128:
1013:. In the three-dimensional case the reduced zone scheme means that from any wavevector
949:
875:
699:
678:
467:
387:
338:
140:
130:
2017:
1885:
1869:
1731:
430:(at zero temperature, this is the maximum kinetic energy the particle can have, i.e.
1735:
1632:
1399:
1124:
882:
Materials with complex crystal structures can have quite intricate Fermi surfaces.
431:
1196:
1132:
887:
852:
863:. When a material's Fermi level falls in a bandgap, there is no Fermi surface.
1614:
1228:
2006:
1861:
1717:
134:
1956:"ARPES experiment in fermiology of quasi-2D metals (Review Article)" (2014)
1808:
1937:
1425:
is related to the cross-section of the Fermi surface (typically given in
1231:. The new states are called Landau levels and are separated by an energy
871:
1787:
1147:
866:
860:
1955:
1836:
1551:
1539:
1529:
865:
116:
101:. The existence of a Fermi surface is a direct consequence of the
739:, the Fermi surface of an ideal Fermi gas is a sphere of radius
1584:
angular correlation of electron positron annihilation radiation
878:
showing the trigonal symmetry of the electron and hole pockets.
18:
1035:
there is an appropriate number of reciprocal lattice vectors
1511:{\displaystyle A_{\perp }={\frac {2\pi e\Delta H}{\hbar c}}}
1963:"Life on the edge: a beginner's guide to the Fermi surface"
1674:"Life on the edge: a beginner's guide to the Fermi surface"
651:
1801:
Electrons in Metals: A short Guide to the Fermi
Surface
827:
determined by the valence electron concentration where
983:
919:
direction. Often in a metal, the Fermi surface radius
1465:
1435:
1408:
1380:
1349:
1329:
1269:
1237:
1205:
1169:
1107:
1085:
1063:
1041:
1019:
958:
925:
896:
833:
748:
708:
681:
560:
531:
495:
470:
439:
412:
390:
363:
341:
306:
197:
167:
143:
731:, the surface of which is called the Fermi surface.
161:, the mean occupation number of a state with energy
1884:
1510:
1448:
1417:
1386:
1362:
1335:
1311:
1255:
1219:
1175:
1115:
1093:
1071:
1049:
1027:
1001:
966:
940:
911:
839:
815:
723:
687:
660:
543:
510:
476:
454:
418:
396:
376:
347:
327:
286:
180:
149:
1765:Electronic Structure and the Properties of Solids
1594:positrons, the momentum distribution for the two
1586:(ACAR) as it measures the angular deviation from
1562:), and, consequently, the Fermi surface, is the
1429:) perpendicular to the magnetic field direction
328:{\displaystyle \left\langle n_{i}\right\rangle }
1887:Fundamentals of Statistical and Thermal Physics
859:or semiconductor depending on the size of the
16:Abstract boundary in condensed matter physics
8:
874:Fermi surface at the corner H points of the
211:
198:
1312:{\displaystyle \omega _{\rm {c}}=eH/m^{*}c}
1009:(in the 1-dimensional case) where a is the
702:, these particles fill up a ball of radius
1998:1983/18576e8a-c769-424d-8ac2-1c52ef80700e
1996:
1986:
1835:
1709:1983/18576e8a-c769-424d-8ac2-1c52ef80700e
1707:
1697:
1643:Fermi surface of superconducting cuprates
1568:Fermi surface of superconducting cuprates
1564:angle-resolved photoemission spectroscopy
1479:
1470:
1464:
1440:
1434:
1407:
1379:
1354:
1348:
1328:
1300:
1291:
1275:
1274:
1268:
1246:
1245:
1236:
1209:
1204:
1168:
1108:
1106:
1086:
1084:
1064:
1062:
1042:
1040:
1020:
1018:
984:
982:
959:
957:
931:
930:
924:
903:
898:
895:
832:
800:
799:
786:
771:
770:
764:
754:
753:
747:
714:
713:
707:
680:
633:
602:
582:
569:
559:
530:
501:
500:
494:
469:
445:
444:
438:
411:
389:
368:
362:
340:
315:
305:
260:
259:
250:
235:
227:
217:
205:
196:
172:
166:
142:
69:Learn how and when to remove this message
32:This article includes a list of general
1664:
1499:
1256:{\displaystyle \hbar \omega _{\rm {c}}}
1238:
1199:. The oscillations are periodic versus
1191:(SdH). The former is an oscillation in
834:
808:
778:
2029:Electric and magnetic fields in matter
1402:proved that the period of oscillation
1824:Journal of Physics: Conference Series
1607:in a 30% alloy was obtained in 1978.
948:is larger than the size of the first
335:is the mean occupation number of the
7:
1942:Experimental Fermi surfaces of some
1928:Experimental Fermi surfaces of some
855:falls in a gap between bands is an
1491:
1409:
1276:
1247:
932:
801:
772:
755:
715:
502:
446:
261:
38:it lacks sufficient corresponding
14:
1582:experimental technique is called
1948:transition metal dichalcogenides
1803:. London: Taylor & Francis.
1617:
1109:
1087:
1065:
1043:
1021:
960:
912:{\displaystyle \mathbf {k} _{z}}
899:
23:
1079:now is closer to the origin in
1002:{\textstyle {\frac {2\pi }{a}}}
1854:10.1088/1742-6596/443/1/012092
1742:. Holt, Rinehart and Winston.
1570:measured by ARPES is shown in
1150:like electrons is governed by
645:
626:
614:
595:
579:
535:
525:Suppose we consider the limit
247:
228:
1:
1988:10.1088/0031-8949/91/5/053009
1961:Dugdale, S. B. (2016-01-01).
1763:Harrison, W. A. (July 1989).
1699:10.1088/0031-8949/91/5/053009
1648:Kelvin probe force microscope
384:is the kinetic energy of the
377:{\displaystyle \epsilon _{i}}
181:{\displaystyle \epsilon _{i}}
1891:. McGraw–Hill. p. 341.
1116:{\displaystyle \mathbf {K} }
1094:{\displaystyle \mathbf {k} }
1072:{\displaystyle \mathbf {k} }
1050:{\displaystyle \mathbf {K} }
1028:{\displaystyle \mathbf {k} }
967:{\displaystyle \mathbf {k} }
1788:VRML Fermi Surface Database
1566:(ARPES). An example of the
941:{\displaystyle k_{\rm {F}}}
724:{\displaystyle k_{\rm {F}}}
511:{\displaystyle k_{\rm {B}}}
455:{\displaystyle E_{\rm {F}}}
97:and from the occupation of
2050:
1952:iron-based superconductors
1449:{\displaystyle A_{\perp }}
1343:is the electronic charge,
1159:Experimental determination
1185:de Haas–van Alphen effect
673:Pauli exclusion principle
103:Pauli exclusion principle
2024:Condensed matter physics
1930:superconducting cuprates
1418:{\displaystyle \Delta H}
1189:Shubnikov–de Haas effect
1057:subtracted that the new
157:particles. According to
83:condensed matter physics
1767:. Courier Corporation.
1193:magnetic susceptibility
1146:The state occupancy of
1137:Jahn–Teller distortions
849:reduced Planck constant
99:electronic energy bands
53:more precise citations.
2034:Fermi–Dirac statistics
1555:
1536:Fermi surface of BSCCO
1520:
1512:
1450:
1419:
1398:. In a famous result,
1388:
1364:
1337:
1313:
1257:
1221:
1177:
1152:Fermi–Dirac statistics
1117:
1095:
1073:
1051:
1029:
1003:
968:
942:
913:
879:
870:Fig. 2: A view of the
841:
840:{\displaystyle \hbar }
817:
725:
689:
662:
545:
544:{\displaystyle T\to 0}
512:
478:
456:
420:
398:
378:
349:
329:
288:
182:
159:Fermi–Dirac statistics
151:
126:
1913:Statistical Mechanics
1799:Ziman, J. M. (1963).
1672:Dugdale, S B (2016).
1605:smeared Fermi surface
1579:positron annihilation
1533:
1513:
1458:
1451:
1420:
1389:
1365:
1363:{\displaystyle m^{*}}
1338:
1314:
1258:
1222:
1178:
1118:
1096:
1074:
1052:
1030:
1004:
969:
943:
914:
869:
842:
818:
726:
690:
663:
546:
513:
479:
457:
421:
399:
379:
350:
330:
289:
183:
152:
120:
1934:strontium ruthenates
1463:
1433:
1406:
1378:
1347:
1327:
1267:
1235:
1203:
1167:
1105:
1083:
1061:
1039:
1017:
981:
956:
923:
894:
831:
746:
706:
679:
558:
529:
493:
486:absolute temperature
468:
437:
419:{\displaystyle \mu }
410:
388:
361:
339:
304:
195:
165:
141:
1979:2016PhyS...91e3009D
1846:2013JPhCS.443a2092W
1740:Solid-State Physics
1690:2016PhyS...91e3009D
1653:Luttinger's theorem
1321:cyclotron frequency
1220:{\displaystyle 1/H}
1101:-space than to any
851:. A material whose
95:crystalline lattice
1950:, ruthenates, and
1560:reciprocal lattice
1556:
1508:
1446:
1415:
1384:
1360:
1333:
1309:
1253:
1217:
1195:and the latter in
1183:, for example the
1173:
1141:spin density waves
1113:
1091:
1069:
1047:
1025:
999:
964:
938:
909:
880:
837:
813:
721:
685:
658:
650:
541:
520:Boltzmann constant
508:
474:
452:
428:chemical potential
416:
394:
374:
345:
325:
284:
178:
147:
127:
89:is the surface in
1898:978-0-07-051800-1
1883:Reif, F. (1965).
1506:
1387:{\displaystyle c}
1336:{\displaystyle e}
1176:{\displaystyle H}
997:
811:
807:
781:
688:{\displaystyle N}
477:{\displaystyle T}
397:{\displaystyle i}
348:{\displaystyle i}
279:
150:{\displaystyle N}
79:
78:
71:
2041:
2010:
2000:
1990:
1916:
1909:
1903:
1902:
1890:
1880:
1874:
1873:
1839:
1819:
1813:
1812:
1796:
1790:
1785:
1779:
1778:
1760:
1754:
1753:
1728:
1722:
1721:
1711:
1701:
1669:
1627:
1622:
1621:
1589:
1517:
1515:
1514:
1509:
1507:
1505:
1497:
1480:
1475:
1474:
1455:
1453:
1452:
1447:
1445:
1444:
1424:
1422:
1421:
1416:
1393:
1391:
1390:
1385:
1370:is the electron
1369:
1367:
1366:
1361:
1359:
1358:
1342:
1340:
1339:
1334:
1318:
1316:
1315:
1310:
1305:
1304:
1295:
1281:
1280:
1279:
1262:
1260:
1259:
1254:
1252:
1251:
1250:
1226:
1224:
1223:
1218:
1213:
1182:
1180:
1179:
1174:
1122:
1120:
1119:
1114:
1112:
1100:
1098:
1097:
1092:
1090:
1078:
1076:
1075:
1070:
1068:
1056:
1054:
1053:
1048:
1046:
1034:
1032:
1031:
1026:
1024:
1011:lattice constant
1008:
1006:
1005:
1000:
998:
993:
985:
973:
971:
970:
965:
963:
947:
945:
944:
939:
937:
936:
935:
918:
916:
915:
910:
908:
907:
902:
886:illustrates the
846:
844:
843:
838:
822:
820:
819:
814:
812:
806:
805:
804:
788:
787:
782:
777:
776:
775:
765:
760:
759:
758:
737:reciprocal space
730:
728:
727:
722:
720:
719:
718:
694:
692:
691:
686:
667:
665:
664:
659:
654:
653:
638:
637:
607:
606:
578:
574:
573:
551:. Then we have,
550:
548:
547:
542:
517:
515:
514:
509:
507:
506:
505:
483:
481:
480:
475:
461:
459:
458:
453:
451:
450:
449:
425:
423:
422:
417:
403:
401:
400:
395:
383:
381:
380:
375:
373:
372:
354:
352:
351:
346:
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332:
331:
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324:
320:
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293:
291:
290:
285:
280:
278:
271:
270:
266:
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254:
240:
239:
218:
210:
209:
187:
185:
184:
179:
177:
176:
156:
154:
153:
148:
91:reciprocal space
74:
67:
63:
60:
54:
49:this article by
40:inline citations
27:
26:
19:
2049:
2048:
2044:
2043:
2042:
2040:
2039:
2038:
2014:
2013:
1967:Physica Scripta
1960:
1925:
1920:
1919:
1910:
1906:
1899:
1882:
1881:
1877:
1821:
1820:
1816:
1798:
1797:
1793:
1786:
1782:
1775:
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1761:
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1750:
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1729:
1725:
1678:Physica Scripta
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1670:
1666:
1661:
1623:
1616:
1613:
1587:
1549:
1498:
1481:
1466:
1461:
1460:
1456:by the equation
1436:
1431:
1430:
1404:
1403:
1376:
1375:
1350:
1345:
1344:
1325:
1324:
1296:
1270:
1265:
1264:
1241:
1233:
1232:
1201:
1200:
1187:(dHvA) and the
1165:
1164:
1161:
1129:superconductors
1103:
1102:
1081:
1080:
1059:
1058:
1037:
1036:
1015:
1014:
986:
979:
978:
954:
953:
926:
921:
920:
897:
892:
891:
829:
828:
795:
766:
749:
744:
743:
709:
704:
703:
677:
676:
649:
648:
629:
624:
618:
617:
598:
593:
583:
565:
561:
556:
555:
527:
526:
496:
491:
490:
466:
465:
440:
435:
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408:
407:
386:
385:
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359:
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337:
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307:
302:
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255:
231:
223:
222:
201:
193:
192:
168:
163:
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139:
138:
115:
75:
64:
58:
55:
45:Please help to
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28:
24:
17:
12:
11:
5:
2047:
2045:
2037:
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2031:
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2016:
2015:
2012:
2011:
1958:
1940:
1924:
1923:External links
1921:
1918:
1917:
1915:(2000), p. 244
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1645:
1640:
1638:Brillouin zone
1635:
1629:
1628:
1625:Physics portal
1612:
1609:
1592:spin polarized
1547:
1544:Brillouin zone
1525:mean free path
1504:
1501:
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1493:
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1484:
1478:
1473:
1469:
1443:
1439:
1414:
1411:
1396:speed of light
1383:
1372:effective mass
1357:
1353:
1332:
1319:is called the
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1303:
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1023:
996:
992:
989:
962:
950:Brillouin zone
934:
929:
906:
901:
876:Brillouin zone
836:
825:
824:
810:
803:
798:
794:
791:
785:
780:
774:
769:
763:
757:
752:
717:
712:
700:momentum space
684:
669:
668:
657:
652:
647:
644:
641:
636:
632:
628:
625:
623:
620:
619:
616:
613:
610:
605:
601:
597:
594:
592:
589:
588:
586:
581:
577:
572:
568:
564:
540:
537:
534:
523:
522:
504:
499:
488:
473:
463:
448:
443:
415:
405:
393:
371:
367:
356:
344:
323:
318:
314:
310:
295:
294:
283:
277:
274:
269:
263:
258:
253:
249:
246:
243:
238:
234:
230:
226:
221:
216:
213:
208:
204:
200:
175:
171:
146:
114:
111:
77:
76:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
2046:
2035:
2032:
2030:
2027:
2025:
2022:
2021:
2019:
2008:
2004:
1999:
1994:
1989:
1984:
1980:
1976:
1973:(5): 053009.
1972:
1968:
1964:
1959:
1957:
1953:
1949:
1945:
1941:
1939:
1935:
1931:
1927:
1926:
1922:
1914:
1908:
1905:
1900:
1894:
1889:
1888:
1879:
1876:
1871:
1867:
1863:
1859:
1855:
1851:
1847:
1843:
1838:
1833:
1830:(1): 012092.
1829:
1825:
1818:
1815:
1810:
1806:
1802:
1795:
1792:
1789:
1784:
1781:
1776:
1774:0-486-66021-4
1770:
1766:
1759:
1756:
1751:
1749:0-03-083993-9
1745:
1741:
1737:
1736:Mermin, N. D.
1733:
1727:
1724:
1719:
1715:
1710:
1705:
1700:
1695:
1691:
1687:
1684:(5): 053009.
1683:
1679:
1675:
1668:
1665:
1658:
1654:
1651:
1649:
1646:
1644:
1641:
1639:
1636:
1634:
1631:
1630:
1626:
1620:
1615:
1610:
1608:
1606:
1601:
1597:
1593:
1585:
1580:
1575:
1573:
1569:
1565:
1561:
1553:
1545:
1541:
1537:
1532:
1528:
1526:
1519:
1502:
1494:
1488:
1485:
1482:
1476:
1471:
1467:
1457:
1441:
1437:
1428:
1412:
1401:
1397:
1381:
1373:
1355:
1351:
1330:
1322:
1306:
1301:
1297:
1292:
1288:
1285:
1282:
1271:
1242:
1230:
1214:
1210:
1206:
1198:
1194:
1190:
1186:
1170:
1158:
1156:
1153:
1149:
1144:
1142:
1138:
1134:
1130:
1126:
1125:ground states
1012:
994:
990:
987:
977:
951:
927:
904:
889:
885:
877:
873:
868:
864:
862:
858:
854:
850:
796:
792:
789:
783:
767:
761:
750:
742:
741:
740:
738:
732:
710:
701:
696:
682:
674:
655:
642:
639:
634:
630:
621:
611:
608:
603:
599:
590:
584:
575:
570:
566:
562:
554:
553:
552:
538:
532:
521:
497:
489:
487:
471:
464:
441:
433:
429:
413:
406:
391:
369:
365:
357:
342:
321:
316:
312:
308:
300:
299:
298:
281:
275:
272:
267:
256:
251:
244:
241:
236:
232:
224:
219:
214:
206:
202:
191:
190:
189:
173:
169:
160:
144:
136:
132:
124:
119:
112:
110:
108:
104:
100:
96:
92:
88:
87:Fermi surface
84:
73:
70:
62:
52:
48:
42:
41:
35:
30:
21:
20:
1970:
1966:
1912:
1907:
1886:
1878:
1827:
1823:
1817:
1800:
1794:
1783:
1764:
1758:
1739:
1732:Ashcroft, N.
1726:
1681:
1677:
1667:
1633:Fermi energy
1604:
1576:
1571:
1557:
1538:measured by
1521:
1459:
1400:Lars Onsager
1162:
1145:
1133:ferromagnets
883:
881:
826:
733:
697:
670:
524:
432:Fermi energy
296:
188:is given by
133:-less ideal
128:
106:
86:
80:
65:
56:
37:
1197:resistivity
888:anisotropic
853:Fermi level
129:Consider a
51:introducing
2018:Categories
1911:K. Huang,
1659:References
1546:of the CuO
1229:Lev Landau
107:fermiology
59:March 2023
34:references
2007:1402-4896
1870:119246268
1862:1742-6596
1837:1304.5363
1718:0031-8949
1550:plane of
1500:ℏ
1492:Δ
1486:π
1472:⊥
1442:⊥
1410:Δ
1356:∗
1302:∗
1272:ω
1243:ω
1239:ℏ
991:π
857:insulator
835:ℏ
809:ℏ
779:ℏ
643:μ
631:ϵ
612:μ
600:ϵ
580:→
536:→
414:μ
366:ϵ
245:μ
242:−
233:ϵ
212:⟩
199:⟨
170:ϵ
135:Fermi gas
1944:cuprates
1738:(1976).
1611:See also
1572:Figure 3
1534:Fig. 3:
1148:fermions
884:Figure 2
872:graphite
695:states.
576:⟩
563:⟨
404:th state
355:th state
322:⟩
309:⟨
1975:Bibcode
1842:Bibcode
1686:Bibcode
1394:is the
861:bandgap
847:is the
671:By the
518:is the
484:is the
426:is the
123:2D ACAR
47:improve
2005:
1895:
1868:
1860:
1809:541173
1807:
1771:
1746:
1716:
1263:where
976:modulo
297:where
113:Theory
85:, the
36:, but
1866:S2CID
1832:arXiv
1577:With
1552:BSCCO
1540:ARPES
2003:ISSN
1932:and
1893:ISBN
1858:ISSN
1805:OCLC
1769:ISBN
1744:ISBN
1714:ISSN
1596:spin
1588:180°
1374:and
1139:and
640:>
609:<
131:spin
1993:hdl
1983:doi
1954:in
1936:in
1850:doi
1828:443
1704:hdl
1694:doi
1600:UHV
698:In
137:of
81:In
2020::
2001:.
1991:.
1981:.
1971:91
1969:.
1965:.
1946:,
1864:.
1856:.
1848:.
1840:.
1826:.
1734:;
1712:.
1702:.
1692:.
1682:91
1680:.
1676:.
1574:.
1518:.
1323:,
1143:.
1135:,
1131:,
109:.
2009:.
1995::
1985::
1977::
1901:.
1872:.
1852::
1844::
1834::
1811:.
1777:.
1752:.
1720:.
1706::
1696::
1688::
1554:.
1548:2
1503:c
1495:H
1489:e
1483:2
1477:=
1468:A
1438:A
1427:Ă…
1413:H
1382:c
1352:m
1331:e
1307:c
1298:m
1293:/
1289:H
1286:e
1283:=
1277:c
1248:c
1215:H
1211:/
1207:1
1171:H
1110:K
1088:k
1066:k
1044:K
1022:k
995:a
988:2
961:k
933:F
928:k
905:z
900:k
823:,
802:F
797:E
793:m
790:2
784:=
773:F
768:p
762:=
756:F
751:k
716:F
711:k
683:N
656:.
646:)
635:i
627:(
622:0
615:)
604:i
596:(
591:1
585:{
571:i
567:n
539:0
533:T
503:B
498:k
472:T
462:)
447:F
442:E
392:i
370:i
343:i
317:i
313:n
282:,
276:1
273:+
268:T
262:B
257:k
252:/
248:)
237:i
229:(
225:e
220:1
215:=
207:i
203:n
174:i
145:N
125:.
72:)
66:(
61:)
57:(
43:.
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