31:
78:
302:
280:
generalizes these ideas. In the limit of very short coherence length the vortex solution is identical to London's fluxoid, where the vortex core is approximated by a sharp cutoff rather than a gradual vanishing of superconducting condensate near the vortex center. Abrikosov found that the vortices
166:
of the superconductor-normal metal boundary. Ginzburg and Landau pointed out the possibility of type-II superconductors that should form inhomogeneous state in strong magnetic fields. However, at that time, all known superconductors were type-I, and they commented that there was no experimental
329:
If a superconductor is cooled in a field, the field can be trapped, which can allow the superconductor to be suspended over a magnet, with the potential for a frictionless joint or bearing. The worth of flux pinning is seen through many implementations such as lifts, frictionless joints, and
73:(a). A mixed state (b), in which some field lines are captured in magnetic field vortices, occurs only in Type-II superconductors within a limited region of the graph. Beyond this region, the superconductive property breaks down, and the material behaves as a normal conductor (c).
489:, they can be easily machined into wires. Recently, however, 2nd generation superconducting tapes are allowing replacement of cheaper niobium-based wires with much more expensive, but superconductive at much higher temperatures and magnetic fields "2nd generation" tapes.
260:. Ginzburg and Landau showed that this leads to negative energy of the interface between superconducting and normal phases. The existence of the negative interface energy was also known since the mid-1930s from the early works by the London brothers. A negative
305:
309:
308:
304:
303:
310:
272:
demonstrated that a magnetic flux can penetrate a superconductor via a topological defect that has integer phase winding and carries quantized magnetic flux. Onsager and
Feynman demonstrated that quantum vortices should form in superfluids.
307:
103:
is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the formation of
264:
suggests that the system should be unstable against maximizing the number of such interfaces. This instability was not observed until the experiments of
Shubnikov in 1936 where two critical fields were found.
258:
285:. Near a so-called upper critical magnetic field, the problem of a superconductor in an external field is equivalent to the problem of vortex state in a rotating superfluid, discussed by
167:
motivation to consider precise structure of type-II superconducting state. The theory for the behavior of the type-II superconducting state in magnetic field was greatly improved by
306:
1230:
697:
963:
900:
831:
938:
1322:
1060:
1170:
609:
1258:
979:
350:
207:
1175:
893:
684:
Abrikosov, A. A. (1957). On the magnetic properties of superconductors of the second group. Soviet
Physics-JETP, 5, 1174-1182.
958:
593:
330:
transportation. The thinner the superconducting layer, the stronger the pinning that occurs when exposed to magnetic fields.
928:
1299:
1151:
1095:
1070:
1201:
1130:
277:
168:
30:
1146:
1065:
444:
933:
203:
155:
217:
1353:
1253:
1248:
886:
953:
626:
Rjabinin, J. N.; Shubnikow, L. W. (1935). "Magnetic
Properties and Critical Currents of Supra-conducting Alloys".
1206:
163:
89:
42:
381:, one of the most common superconductors in applied superconductivity), as well as intermetallic compounds like
989:
211:
1040:
1332:
1191:
1123:
1243:
1216:
1196:
389:
192:
396:
ceramic materials which have achieved the highest superconducting critical temperatures. These include La
1113:
323:
159:
1317:
378:
377:
are also type-II superconductors. Metal alloy superconductors can also exhibit type-II behavior (e.g.,
1273:
772:
719:
635:
540:
505:
Wells, Frederick S.; Pan, Alexey V.; Wang, X. Renshaw; Fedoseev, Sergey A.; Hilgenkamp, Hans (2015).
464:
69:
are labeled. In the lower region of this graph, both type-I and type-II superconductors display the
1304:
1055:
1015:
814:
Feynman, R.P. (1955), "Application of
Quantum Mechanics to Liquid Helium", in WP Halperin (ed.),
796:
651:
530:
437:
432:), which is famous as the first material to achieve superconductivity above the boiling point of
142:
experimentally discovered the type-II superconductors. In 1950, the theory of the two types of
27:
Superconductor characterized by the formation of magnetic vortices in an applied magnetic field
1080:
909:
827:
788:
589:
566:
96:
1289:
1263:
1035:
1010:
943:
819:
780:
727:
643:
556:
548:
468:
261:
105:
1312:
846:
382:
1045:
433:
290:
176:
151:
143:
127:
119:. The vortex density increases with increasing field strength. At a higher critical field
70:
475:
wires. These materials are type-II superconductors with substantial upper critical field
776:
723:
710:
London, F. (1948-09-01). "On the
Problem of the Molecular Theory of Superconductivity".
639:
544:
1050:
994:
984:
948:
561:
506:
109:
81:
34:
Superconductive behavior under varying magnetic field and temperature. The graph shows
17:
823:
268:
In 1952 an observation of type-II superconductivity was also reported by
Zavaritskii.
1347:
800:
343:
188:
139:
35:
126:, superconductivity is destroyed. Type-II superconductors do not exhibit a complete
1085:
1075:
1030:
1025:
655:
440:
319:
286:
269:
184:
172:
1211:
1020:
482:, and in contrast to, for example, the cuprate superconductors with even higher
472:
183:. Quantum vortex solution in a superconductor is also very closely related to
180:
923:
393:
362:
353:
are type-II superconductors. While most elemental superconductors are type-I,
147:
792:
507:"Analysis of low-field isotropic vortex glass containing vortex groups in YBa
869:
Rosen, J., Ph.D., & Quinn, L. "Superconductivity". In K. Cullen (ed.),
731:
570:
77:
314:
Position memory due to vortex pinning in a high temperature superconductor
1238:
358:
784:
417:
374:
370:
354:
346:
552:
647:
429:
425:
421:
339:
878:
610:
Magnetic properties and critical currents of superconducting alloys
535:
214:. According to Ginzburg–Landau theory, in a type-II superconductor
1294:
1268:
409:
366:
300:
76:
195:
was awarded for the theory of type-II superconductivity in 2003.
1327:
413:
85:
882:
460:
456:
763:
Onsager, L. (March 1949). "Statistical hydrodynamics".
326:, since they cannot be penetrated by magnetic fields.
112:. This occurs above a certain critical field strength
220:
1282:
1229:
1184:
1160:
1139:
1103:
1094:
1003:
972:
916:
519:
thin films visualized by scanning SQUID microscopy"
281:arrange themselves into a regular array known as a
338:Type-II superconductors are usually made of metal
252:
847:"Journal of Experimental and Theoretical Physics"
586:Introduction to Superconductivity, Second Edition
698:"Type II superconductors and the vortex lattice"
455:Strong superconducting electromagnets (used in
253:{\displaystyle \lambda /\xi >1/{\sqrt {2}}}
894:
608:Rjabinin, J. N. and Schubnikow, L.W. (1935) "
8:
322:becomes possible. This is not possible with
692:
690:
318:In the vortex state, a phenomenon known as
1100:
901:
887:
879:
818:, vol. 1, Elsevier, pp. 17–53,
614:Physikalische Zeitschrift der Sowjetunion
560:
534:
243:
238:
224:
219:
212:London magnetic field penetration depth λ
29:
668:Ginzburg, V.L. and Landau, L.D. (1950)
497:
365:are elemental type-II superconductors.
171:, who was elaborating on the ideas by
191:quantization in superconductors. The
7:
743:
741:
816:Progress in Low Temperature Physics
48:. Critical magnetic flux densities
25:
700:, Nobel Lecture, December 8, 2003
871:Encyclopedia of physical science
752:(2nd ed.). New York: Dover.
351:high-temperature superconductors
208:superconducting coherence length
388:Other type-II examples are the
1:
824:10.1016/s0079-6417(08)60077-3
588:. New York, NY: McGraw-Hill.
471:wires or, for higher fields,
62:and the critical temperature
616:, vol. 7, no.1, pp. 122–125.
445:ideally hard superconductors
443:, the cuprates are close to
169:Alexei Alexeyevich Abrikosov
467:) often use coils wound of
138:In 1935, J.N. Rjabinin and
1370:
1231:Technological applications
973:Characteristic parameters
146:was further developed by
108:with an applied external
90:scanning SQUID microscopy
990:London penetration depth
1283:List of superconductors
1161:By critical temperature
179:of quantum vortices in
158:. In their argument, a
106:magnetic field vortices
18:Type-II superconductors
748:London, Fritz (1961).
732:10.1103/PhysRev.74.562
436:(77 K). Due to strong
324:type-I superconductors
315:
254:
204:Ginzburg–Landau theory
193:Nobel Prize in Physics
156:Ginzburg–Landau theory
101:type-II superconductor
92:
74:
929:Bean's critical state
465:particle accelerators
313:
255:
160:type-I superconductor
80:
33:
1104:By magnetic response
670:Zh. Eksp. Teor. Fiz.
584:Tinkham, M. (1996).
218:
43:absolute temperature
1056:persistent currents
1041:Little–Parks effect
777:1949NCim....6S.279O
724:1948PhRv...74..562L
640:1935Natur.135..581R
545:2015NatSR...5E8677W
1016:Andreev reflection
1011:Abrikosov vortices
785:10.1007/BF02780991
523:Scientific Reports
316:
250:
154:in their paper on
93:
84:in a 200-nm-thick
75:
1354:Superconductivity
1341:
1340:
1259:quantum computing
1225:
1224:
1081:superdiamagnetism
910:Superconductivity
833:978-0-444-53307-4
696:A. A. Abrikosov,
553:10.1038/srep08677
311:
248:
210:Îľ in addition to
97:superconductivity
41:as a function of
16:(Redirected from
1361:
1290:bilayer graphene
1264:Rutherford cable
1176:room temperature
1171:high temperature
1101:
1061:proximity effect
1036:Josephson effect
980:coherence length
903:
896:
889:
880:
874:
867:
861:
860:
858:
857:
843:
837:
836:
811:
805:
804:
765:Il Nuovo Cimento
760:
754:
753:
745:
736:
735:
707:
701:
694:
685:
682:
676:
666:
660:
659:
648:10.1038/135581a0
623:
617:
606:
600:
599:
581:
575:
574:
564:
538:
502:
469:niobium-titanium
379:niobium–titanium
312:
276:A 1957 paper by
262:interface energy
259:
257:
256:
251:
249:
244:
242:
228:
82:Quantum vortices
21:
1369:
1368:
1364:
1363:
1362:
1360:
1359:
1358:
1344:
1343:
1342:
1337:
1308:
1278:
1221:
1180:
1167:low temperature
1156:
1135:
1090:
1046:Meissner effect
999:
995:Silsbee current
968:
934:Ginzburg–Landau
912:
907:
877:
868:
864:
855:
853:
845:
844:
840:
834:
813:
812:
808:
771:(S2): 279–287.
762:
761:
757:
747:
746:
739:
712:Physical Review
709:
708:
704:
695:
688:
683:
679:
667:
663:
625:
624:
620:
607:
603:
596:
583:
582:
578:
518:
514:
510:
504:
503:
499:
495:
487:
480:
453:
434:liquid nitrogen
407:
403:
399:
336:
301:
299:
291:Richard Feynman
278:A. A. Abrikosov
216:
215:
206:introduced the
201:
177:Richard Feynman
152:Vitaly Ginzburg
144:superconductors
136:
128:Meissner effect
124:
117:
88:film imaged by
71:Meissner effect
67:
60:
53:
28:
23:
22:
15:
12:
11:
5:
1367:
1365:
1357:
1356:
1346:
1345:
1339:
1338:
1336:
1335:
1330:
1325:
1320:
1315:
1310:
1306:
1302:
1297:
1292:
1286:
1284:
1280:
1279:
1277:
1276:
1271:
1266:
1261:
1256:
1251:
1246:
1244:electromagnets
1241:
1235:
1233:
1227:
1226:
1223:
1222:
1220:
1219:
1214:
1209:
1204:
1199:
1194:
1188:
1186:
1185:By composition
1182:
1181:
1179:
1178:
1173:
1168:
1164:
1162:
1158:
1157:
1155:
1154:
1152:unconventional
1149:
1143:
1141:
1140:By explanation
1137:
1136:
1134:
1133:
1128:
1127:
1126:
1121:
1116:
1107:
1105:
1098:
1096:Classification
1092:
1091:
1089:
1088:
1083:
1078:
1073:
1068:
1063:
1058:
1053:
1048:
1043:
1038:
1033:
1028:
1023:
1018:
1013:
1007:
1005:
1001:
1000:
998:
997:
992:
987:
985:critical field
982:
976:
974:
970:
969:
967:
966:
961:
956:
954:Mattis–Bardeen
951:
946:
941:
939:Kohn–Luttinger
936:
931:
926:
920:
918:
914:
913:
908:
906:
905:
898:
891:
883:
876:
875:
862:
851:www.jetp.ac.ru
838:
832:
806:
755:
737:
718:(5): 562–573.
702:
686:
677:
661:
618:
601:
594:
576:
516:
512:
508:
496:
494:
491:
485:
478:
463:machines, and
452:
451:Important uses
449:
405:
401:
397:
335:
332:
298:
295:
283:vortex lattice
247:
241:
237:
234:
231:
227:
223:
200:
197:
135:
132:
122:
115:
110:magnetic field
65:
58:
51:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1366:
1355:
1352:
1351:
1349:
1334:
1331:
1329:
1326:
1324:
1321:
1319:
1316:
1314:
1311:
1309:
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1287:
1285:
1281:
1275:
1272:
1270:
1267:
1265:
1262:
1260:
1257:
1255:
1252:
1250:
1247:
1245:
1242:
1240:
1237:
1236:
1234:
1232:
1228:
1218:
1215:
1213:
1210:
1208:
1205:
1203:
1202:heavy fermion
1200:
1198:
1195:
1193:
1190:
1189:
1187:
1183:
1177:
1174:
1172:
1169:
1166:
1165:
1163:
1159:
1153:
1150:
1148:
1145:
1144:
1142:
1138:
1132:
1131:ferromagnetic
1129:
1125:
1122:
1120:
1117:
1115:
1112:
1111:
1109:
1108:
1106:
1102:
1099:
1097:
1093:
1087:
1084:
1082:
1079:
1077:
1076:supercurrents
1074:
1072:
1069:
1067:
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1047:
1044:
1042:
1039:
1037:
1034:
1032:
1029:
1027:
1024:
1022:
1019:
1017:
1014:
1012:
1009:
1008:
1006:
1002:
996:
993:
991:
988:
986:
983:
981:
978:
977:
975:
971:
965:
962:
960:
957:
955:
952:
950:
947:
945:
942:
940:
937:
935:
932:
930:
927:
925:
922:
921:
919:
915:
911:
904:
899:
897:
892:
890:
885:
884:
881:
872:
866:
863:
852:
848:
842:
839:
835:
829:
825:
821:
817:
810:
807:
802:
798:
794:
790:
786:
782:
778:
774:
770:
766:
759:
756:
751:
744:
742:
738:
733:
729:
725:
721:
717:
713:
706:
703:
699:
693:
691:
687:
681:
678:
674:
671:
665:
662:
657:
653:
649:
645:
641:
637:
634:(3415): 581.
633:
629:
622:
619:
615:
611:
605:
602:
597:
591:
587:
580:
577:
572:
568:
563:
558:
554:
550:
546:
542:
537:
532:
528:
524:
520:
501:
498:
492:
490:
488:
481:
474:
470:
466:
462:
458:
450:
448:
446:
442:
439:
435:
431:
427:
423:
419:
415:
411:
395:
391:
386:
384:
380:
376:
372:
368:
364:
360:
356:
352:
348:
345:
344:complex oxide
341:
333:
331:
327:
325:
321:
296:
294:
292:
288:
284:
279:
274:
271:
266:
263:
245:
239:
235:
232:
229:
225:
221:
213:
209:
205:
198:
196:
194:
190:
189:magnetic flux
186:
182:
178:
174:
170:
165:
162:had positive
161:
157:
153:
149:
145:
141:
140:Lev Shubnikov
133:
131:
129:
125:
118:
111:
107:
102:
98:
91:
87:
83:
79:
72:
68:
61:
54:
47:
44:
40:
37:
36:magnetic flux
32:
19:
1212:oxypnictides
1147:conventional
1118:
1086:superstripes
1031:flux pumping
1026:flux pinning
1021:Cooper pairs
870:
865:
854:. Retrieved
850:
841:
815:
809:
768:
764:
758:
749:
715:
711:
705:
680:
672:
669:
664:
631:
627:
621:
613:
604:
585:
579:
526:
522:
500:
483:
476:
454:
387:
337:
328:
320:flux pinning
317:
297:Flux pinning
287:Lars Onsager
282:
275:
270:Fritz London
267:
202:
199:Vortex state
185:Fritz London
173:Lars Onsager
137:
120:
113:
100:
94:
63:
56:
49:
45:
38:
1071:SU(2) color
1051:Homes's law
750:Superfluids
473:niobium-tin
383:niobium–tin
187:'s work on
181:superfluids
164:free energy
1207:iron-based
1066:reentrance
856:2021-04-11
595:0486435032
536:1807.06746
493:References
459:scanners,
394:perovskite
363:technetium
148:Lev Landau
1004:Phenomena
801:186224016
793:0029-6341
517:7−x
334:Materials
230:ξ
222:λ
1348:Category
1239:cryotron
1197:cuprates
1192:covalent
949:Matthias
917:Theories
571:25728772
529:: 8677.
359:vanadium
347:ceramics
1333:more...
1217:organic
773:Bibcode
720:Bibcode
656:4113840
636:Bibcode
562:4345321
541:Bibcode
441:pinning
418:Yttrium
390:cuprate
375:silicon
371:diamond
369:-doped
355:niobium
134:History
1110:Types
944:London
830:
799:
791:
675:, 1064
654:
628:Nature
592:
569:
559:
438:vortex
426:Copper
422:Barium
412:, and
361:, and
349:. All
340:alloys
1323:TBCCO
1295:BSCCO
1274:wires
1269:SQUID
797:S2CID
652:S2CID
531:arXiv
430:Oxide
410:BSCCO
367:Boron
1328:YBCO
1318:NbTi
1313:NbSn
1300:LBCO
828:ISBN
789:ISSN
590:ISBN
567:PMID
414:YBCO
402:0.15
398:1.85
373:and
289:and
233:>
175:and
150:and
99:, a
86:YBCO
55:and
1305:MgB
1254:NMR
1249:MRI
1124:1.5
964:WHH
959:RVB
924:BCS
820:doi
781:doi
728:doi
644:doi
632:135
612:",
557:PMC
549:doi
461:NMR
457:MRI
404:CuO
342:or
293:.
95:In
1350::
1119:II
849:.
826:,
795:.
787:.
779:.
767:.
740:^
726:.
716:74
714:.
689:^
673:20
650:.
642:.
630:.
565:.
555:.
547:.
539:.
525:.
521:.
511:Cu
486:c2
479:c2
447:.
408:,
400:Ba
385:.
357:,
130:.
123:c2
116:c1
59:C2
52:C1
1307:2
1114:I
902:e
895:t
888:v
873:.
859:.
822::
803:.
783::
775::
769:6
734:.
730::
722::
658:.
646::
638::
598:.
573:.
551::
543::
533::
527:5
515:O
513:3
509:2
484:H
477:H
428:-
424:-
420:-
416:(
406:4
392:-
246:2
240:/
236:1
226:/
121:H
114:H
66:C
64:T
57:B
50:B
46:T
39:B
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
