28:
374:
240:
779:. Abrikosov vortices form a lattice, usually triangular, with the average vortex density (flux density) approximately equal to the externally applied magnetic field. As with other lattices, defects may form as dislocations.
601:
192:
497:
649:
369:{\displaystyle B(r)={\frac {\Phi _{0}}{2\pi \lambda ^{2}}}K_{0}\left({\frac {r}{\lambda }}\right)\approx {\sqrt {\frac {\lambda }{r}}}\exp \left(-{\frac {r}{\lambda }}\right),}
523:
752:), the field penetrates into superconductor in terms of Abrikosov vortices. Each vortex obeys London's magnetic flux quantization and carries one quantum of magnetic flux
777:
226:
119:
412:
147:
750:
717:
442:
1459:
684:
1192:
1129:
896:
530:
1095:
1065:
1167:
1551:
1289:
235:
The magnetic field distribution of a single vortex far from its core can be described by the same equation as in the London's fluxoid
1399:
1487:
1208:
122:
1404:
1122:
1187:
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1528:
1380:
1324:
1299:
789:
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1359:
65:
1375:
1294:
1162:
126:
69:
1582:
1482:
1477:
1115:
1182:
794:
159:
1435:
447:
36:
1218:
150:
1269:
616:
1561:
1420:
1352:
154:
1472:
1445:
1425:
1347:
663:
659:
652:
61:
1342:
199:
1546:
1502:
1004:
945:
905:
850:
815:
Wells, Frederick S.; Pan, Alexey V.; Wang, X. Renshaw; Fedoseev, Sergey A.; Hilgenkamp, Hans (2015).
720:
687:
68:
to explain magnetic behavior of type-II superconductors. Abrikosov vortices occur generically in the
502:
1533:
1284:
1244:
1047:
1028:
840:
98:
circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size
755:
204:
101:
1587:
1309:
1138:
1091:
1061:
1020:
876:
381:
132:
1518:
1492:
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1053:
1012:
953:
913:
866:
858:
725:
692:
421:
1541:
1274:
415:
1008:
949:
936:
London, F. (1948-09-01). "On the
Problem of the Molecular Theory of Superconductivity".
909:
854:
1279:
1223:
1213:
1177:
871:
816:
669:
1057:
1576:
1032:
917:
1314:
1304:
1259:
1254:
195:
95:
85:
81:
57:
17:
1440:
1249:
1152:
1052:, Progress in Low Temperature Physics, vol. 1, Elsevier, pp. 17–53,
992:
894:
Abrikosov, A. A. (1957). "The magnetic properties of superconducting alloys".
596:{\displaystyle B(0)\approx {\frac {\Phi _{0}}{2\pi \lambda ^{2}}}\ln \kappa ,}
1024:
817:"Analysis of low-field isotropic vortex glass containing vortex groups in YBa
957:
880:
27:
1467:
1016:
862:
229:
44:
1107:
845:
1523:
1497:
26:
1556:
32:
1111:
198:
induce magnetic fields with the total flux equal to a single
1049:
Chapter II Application of
Quantum Mechanics to Liquid Helium
613:
is known as the
Ginzburg–Landau parameter, which must be
84:, combined with a concept of core of quantum vortex by
666:
contains no vortices, and one applies a magnetic field
1090:. Addison Wesley Publishing Company, Inc. p. 59.
758:
728:
695:
672:
619:
533:
505:
450:
424:
384:
243:
207:
162:
135:
104:
80:
The solution is a combination of fluxon solution by
1511:
1458:
1413:
1389:
1368:
1332:
1323:
1232:
1201:
1145:
829:
thin films visualized by scanning SQUID microscopy"
228:. Therefore, an Abrikosov vortex is often called a
771:
744:
711:
678:
643:
595:
517:
491:
436:
406:
368:
220:
186:
141:
113:
499:, i.e. logarithmically diverges. In reality, for
129:). The supercurrents decay on the distance about
418:. Note that, according to the above formula, at
662:by chance, on defects, etc. Even if initially
1123:
8:
187:{\displaystyle \lambda >\xi /{\sqrt {2}}}
492:{\displaystyle B(r)\propto \ln(\lambda /r)}
1329:
1130:
1116:
1108:
897:Journal of Physics and Chemistry of Solids
870:
844:
763:
757:
733:
727:
700:
694:
671:
634:
629:
618:
572:
555:
549:
532:
504:
478:
449:
423:
389:
383:
348:
322:
305:
295:
282:
265:
259:
242:
212:
206:
177:
172:
161:
134:
103:
644:{\displaystyle \kappa >1/{\sqrt {2}}}
807:
658:Abrikosov vortices can be trapped in a
1088:Superconductivity of Metals and Alloys
7:
980:(2nd ed.). New York, NY: Dover.
971:
969:
967:
931:
929:
927:
1086:de Gennes, Pierre-Gilles (2018) .
760:
552:
262:
209:
25:
123:superconducting coherence length
543:
537:
518:{\displaystyle r\lesssim \xi }
486:
472:
460:
454:
428:
401:
395:
253:
247:
153:) from the core. Note that in
1:
1058:10.1016/s0079-6417(08)60077-3
790:Macroscopic quantum phenomena
525:the field is simply given by
918:10.1016/0022-3697(57)90083-5
993:"Statistical hydrodynamics"
31:Vortices in a 200-nm-thick
1604:
1460:Technological applications
991:Onsager, L. (March 1949).
1202:Characteristic parameters
772:{\displaystyle \Phi _{0}}
221:{\displaystyle \Phi _{0}}
114:{\displaystyle \sim \xi }
37:scanning SQUID microscopy
1219:London penetration depth
407:{\displaystyle K_{0}(z)}
151:London penetration depth
142:{\displaystyle \lambda }
42:In superconductivity, a
1512:List of superconductors
1390:By critical temperature
653:type-II superconductors
155:type-II superconductors
1046:Feynman, R.P. (1955),
976:London, Fritz (1961).
958:10.1103/PhysRev.74.562
773:
746:
745:{\displaystyle H_{c2}}
719:(but smaller than the
713:
712:{\displaystyle H_{c1}}
680:
664:type-II superconductor
660:type-II superconductor
645:
597:
519:
493:
438:
437:{\displaystyle r\to 0}
408:
370:
222:
188:
143:
127:Ginzburg–Landau theory
115:
72:of superconductivity.
70:Ginzburg–Landau theory
62:type-II superconductor
39:
1158:Bean's critical state
795:Nielsen–Olesen vortex
774:
747:
714:
681:
646:
598:
520:
494:
439:
409:
371:
223:
189:
144:
116:
91:In the quantum vortex
30:
1333:By magnetic response
756:
726:
721:upper critical field
693:
688:lower critical field
670:
617:
531:
503:
448:
422:
382:
241:
205:
160:
133:
102:
1285:persistent currents
1270:Little–Parks effect
1009:1949NCim....6S.279O
950:1948PhRv...74..562L
910:1957JPCS....2..199A
855:2015NatSR...5E8677W
444:the magnetic field
1245:Andreev reflection
1240:Abrikosov vortices
1017:10.1007/BF02780991
833:Scientific Reports
769:
742:
709:
676:
641:
593:
515:
489:
434:
414:is a zeroth-order
404:
366:
218:
194:. The circulating
184:
139:
111:
40:
18:Abrikosov vortices
1583:Superconductivity
1570:
1569:
1488:quantum computing
1454:
1453:
1310:superdiamagnetism
1139:Superconductivity
1097:978-0-7382-0101-6
1067:978-0-444-53307-4
863:10.1038/srep08677
679:{\displaystyle H}
639:
579:
356:
332:
331:
313:
289:
182:
56:) is a vortex of
16:(Redirected from
1595:
1519:bilayer graphene
1493:Rutherford cable
1405:room temperature
1400:high temperature
1330:
1290:proximity effect
1265:Josephson effect
1209:coherence length
1132:
1125:
1118:
1109:
1102:
1101:
1083:
1077:
1076:
1075:
1074:
1043:
1037:
1036:
997:Il Nuovo Cimento
988:
982:
981:
973:
962:
961:
933:
922:
921:
891:
885:
884:
874:
848:
812:
778:
776:
775:
770:
768:
767:
751:
749:
748:
743:
741:
740:
718:
716:
715:
710:
708:
707:
686:larger than the
685:
683:
682:
677:
650:
648:
647:
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602:
600:
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560:
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482:
443:
441:
440:
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413:
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349:
333:
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193:
191:
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185:
183:
178:
176:
148:
146:
145:
140:
125:(parameter of a
120:
118:
117:
112:
66:Alexei Abrikosov
50:Abrikosov vortex
48:(also called an
21:
1603:
1602:
1598:
1597:
1596:
1594:
1593:
1592:
1573:
1572:
1571:
1566:
1537:
1507:
1450:
1409:
1396:low temperature
1385:
1364:
1319:
1275:Meissner effect
1228:
1224:Silsbee current
1197:
1163:Ginzburg–Landau
1141:
1136:
1106:
1105:
1098:
1085:
1084:
1080:
1072:
1070:
1068:
1045:
1044:
1040:
1003:(S2): 279–287.
990:
989:
985:
975:
974:
965:
938:Physical Review
935:
934:
925:
893:
892:
888:
828:
824:
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724:
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668:
667:
615:
614:
603:
568:
561:
551:
529:
528:
501:
500:
446:
445:
420:
419:
416:Bessel function
385:
380:
379:
376:
344:
340:
301:
291:
278:
271:
261:
239:
238:
208:
203:
202:
158:
157:
131:
130:
100:
99:
94:
78:
35:film imaged by
23:
22:
15:
12:
11:
5:
1601:
1599:
1591:
1590:
1585:
1575:
1574:
1568:
1567:
1565:
1564:
1559:
1554:
1549:
1544:
1539:
1535:
1531:
1526:
1521:
1515:
1513:
1509:
1508:
1506:
1505:
1500:
1495:
1490:
1485:
1480:
1475:
1473:electromagnets
1470:
1464:
1462:
1456:
1455:
1452:
1451:
1449:
1448:
1443:
1438:
1433:
1428:
1423:
1417:
1415:
1414:By composition
1411:
1410:
1408:
1407:
1402:
1397:
1393:
1391:
1387:
1386:
1384:
1383:
1381:unconventional
1378:
1372:
1370:
1369:By explanation
1366:
1365:
1363:
1362:
1357:
1356:
1355:
1350:
1345:
1336:
1334:
1327:
1325:Classification
1321:
1320:
1318:
1317:
1312:
1307:
1302:
1297:
1292:
1287:
1282:
1277:
1272:
1267:
1262:
1257:
1252:
1247:
1242:
1236:
1234:
1230:
1229:
1227:
1226:
1221:
1216:
1214:critical field
1211:
1205:
1203:
1199:
1198:
1196:
1195:
1190:
1185:
1183:Mattis–Bardeen
1180:
1175:
1170:
1168:Kohn–Luttinger
1165:
1160:
1155:
1149:
1147:
1143:
1142:
1137:
1135:
1134:
1127:
1120:
1112:
1104:
1103:
1096:
1078:
1066:
1038:
983:
963:
944:(5): 562–573.
923:
904:(3): 199–208.
886:
826:
822:
818:
806:
805:
803:
800:
798:
797:
792:
786:
784:
781:
766:
762:
739:
736:
732:
706:
703:
699:
675:
638:
632:
628:
625:
622:
592:
589:
586:
583:
575:
571:
567:
564:
558:
554:
548:
545:
542:
539:
536:
527:
514:
511:
508:
488:
485:
481:
477:
474:
471:
468:
465:
462:
459:
456:
453:
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427:
403:
400:
397:
392:
388:
365:
361:
355:
352:
347:
343:
339:
336:
330:
327:
321:
317:
312:
309:
304:
298:
294:
285:
281:
277:
274:
268:
264:
258:
255:
252:
249:
246:
237:
215:
211:
181:
175:
171:
168:
165:
138:
110:
107:
92:
77:
74:
54:quantum vortex
24:
14:
13:
10:
9:
6:
4:
3:
2:
1600:
1589:
1586:
1584:
1581:
1580:
1578:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1543:
1540:
1538:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1516:
1514:
1510:
1504:
1501:
1499:
1496:
1494:
1491:
1489:
1486:
1484:
1481:
1479:
1476:
1474:
1471:
1469:
1466:
1465:
1463:
1461:
1457:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1431:heavy fermion
1429:
1427:
1424:
1422:
1419:
1418:
1416:
1412:
1406:
1403:
1401:
1398:
1395:
1394:
1392:
1388:
1382:
1379:
1377:
1374:
1373:
1371:
1367:
1361:
1360:ferromagnetic
1358:
1354:
1351:
1349:
1346:
1344:
1341:
1340:
1338:
1337:
1335:
1331:
1328:
1326:
1322:
1316:
1313:
1311:
1308:
1306:
1305:supercurrents
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1286:
1283:
1281:
1278:
1276:
1273:
1271:
1268:
1266:
1263:
1261:
1258:
1256:
1253:
1251:
1248:
1246:
1243:
1241:
1238:
1237:
1235:
1231:
1225:
1222:
1220:
1217:
1215:
1212:
1210:
1207:
1206:
1204:
1200:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1156:
1154:
1151:
1150:
1148:
1144:
1140:
1133:
1128:
1126:
1121:
1119:
1114:
1113:
1110:
1099:
1093:
1089:
1082:
1079:
1069:
1063:
1059:
1055:
1051:
1050:
1042:
1039:
1034:
1030:
1026:
1022:
1018:
1014:
1010:
1006:
1002:
998:
994:
987:
984:
979:
972:
970:
968:
964:
959:
955:
951:
947:
943:
939:
932:
930:
928:
924:
919:
915:
911:
907:
903:
899:
898:
890:
887:
882:
878:
873:
868:
864:
860:
856:
852:
847:
842:
838:
834:
830:
811:
808:
801:
796:
793:
791:
788:
787:
782:
780:
764:
737:
734:
730:
722:
704:
701:
697:
689:
673:
665:
661:
656:
654:
636:
630:
626:
623:
620:
612:
608:
590:
587:
584:
581:
573:
569:
565:
562:
556:
546:
540:
534:
526:
512:
509:
506:
483:
479:
475:
469:
466:
463:
457:
451:
431:
425:
417:
398:
390:
386:
363:
359:
353:
350:
345:
341:
337:
334:
328:
325:
319:
315:
310:
307:
302:
296:
292:
283:
279:
275:
272:
266:
256:
250:
244:
236:
233:
231:
213:
201:
197:
196:supercurrents
179:
173:
169:
166:
163:
156:
152:
136:
128:
124:
108:
105:
97:
89:
87:
83:
75:
73:
71:
67:
63:
59:
55:
51:
47:
46:
38:
34:
29:
19:
1441:oxypnictides
1376:conventional
1315:superstripes
1260:flux pumping
1255:flux pinning
1250:Cooper pairs
1239:
1087:
1081:
1071:, retrieved
1048:
1041:
1000:
996:
986:
977:
941:
937:
901:
895:
889:
836:
832:
810:
657:
610:
606:
604:
377:
234:
200:flux quantum
96:supercurrent
90:
86:Lars Onsager
82:Fritz London
79:
58:supercurrent
53:
49:
43:
41:
1300:SU(2) color
1280:Homes's law
978:Superfluids
64:, used by
1577:Categories
1436:iron-based
1295:reentrance
1073:2021-04-11
846:1807.06746
802:References
1233:Phenomena
1033:186224016
1025:0029-6341
827:7−x
761:Φ
621:κ
588:κ
585:
570:λ
566:π
553:Φ
547:≈
513:ξ
510:≲
476:λ
470:
464:∝
429:→
354:λ
346:−
338:
326:λ
320:≈
311:λ
280:λ
276:π
263:Φ
210:Φ
170:ξ
164:λ
137:λ
109:ξ
106:∼
1588:Vortices
1468:cryotron
1426:cuprates
1421:covalent
1178:Matthias
1146:Theories
881:25728772
839:: 8677.
783:See also
76:Overview
1562:more...
1446:organic
1005:Bibcode
946:Bibcode
906:Bibcode
872:4345321
851:Bibcode
1339:Types
1173:London
1094:
1064:
1031:
1023:
879:
869:
605:where
378:where
230:fluxon
121:— the
45:fluxon
1552:TBCCO
1524:BSCCO
1503:wires
1498:SQUID
1029:S2CID
841:arXiv
60:in a
1557:YBCO
1547:NbTi
1542:NbSn
1529:LBCO
1092:ISBN
1062:ISBN
1021:ISSN
877:PMID
624:>
167:>
33:YBCO
1534:MgB
1483:NMR
1478:MRI
1353:1.5
1193:WHH
1188:RVB
1153:BCS
1054:doi
1013:doi
954:doi
914:doi
867:PMC
859:doi
651:in
611:λ/ξ
335:exp
52:or
1579::
1348:II
1060:,
1027:.
1019:.
1011:.
999:.
995:.
966:^
952:.
942:74
940:.
926:^
912:.
900:.
875:.
865:.
857:.
849:.
835:.
831:.
821:Cu
655:.
609:=
582:ln
467:ln
232:.
88:.
1536:2
1343:I
1131:e
1124:t
1117:v
1100:.
1056::
1035:.
1015::
1007::
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