3596:
461:
258:
7464:
7892:
7916:
926:
5357:
7928:
7904:
75:
25:
1223:
666:
5132:
4429:
955:
4572:
2042:
2734:
1437:
4150:
102:, where the effects of quantum mechanics are observable at ordinary, rather than atomic, scale. The Josephson effect has many practical applications because it exhibits a precise relationship between different physical measures, such as voltage and frequency, facilitating highly accurate measurements.
185:
and Hans
Meissner, and theoretical work by Robert Parmenter. Pippard initially believed that the tunneling effect was possible but that it would be too small to be noticeable, but Josephson did not agree, especially after Anderson introduced him to a preprint of "Superconductive Tunneling" by Cohen,
180:
employee on sabbatical leave for the 1961–1962 academic year. The course introduced
Josephson to the idea of broken symmetry in superconductors, and he "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally". Josephson studied the
6780:
6269:
2436:
1824:
1653:
921:{\displaystyle i\hbar {\frac {\partial }{\partial t}}{\begin{pmatrix}{\sqrt {n_{A}}}e^{i\phi _{A}}\\{\sqrt {n_{B}}}e^{i\phi _{B}}\end{pmatrix}}={\begin{pmatrix}eV&K\\K&-eV\end{pmatrix}}{\begin{pmatrix}{\sqrt {n_{A}}}e^{i\phi _{A}}\\{\sqrt {n_{B}}}e^{i\phi _{B}}\end{pmatrix}},}
4704:
5352:{\displaystyle \Delta E=\int _{1}^{2}IV\operatorname {d} \!{t}=\int _{1}^{2}I\operatorname {d} \!\Phi =\int _{\varphi _{1}}^{\varphi _{2}}I_{c}\sin \varphi \operatorname {d} \!\left(\Phi _{0}{\frac {\varphi }{2\pi }}\right)=-{\frac {\Phi _{0}I_{c}}{2\pi }}\Delta \cos \varphi \,.}
5846:
1869:
4275:
2557:
1232:
4899:
Note that although the kinetic behavior of the
Josephson junction is similar to that of an inductor, there is no associated magnetic field. This behaviour is derived from the kinetic energy of the charge carriers, instead of the energy in a magnetic field.
193:
We were all—Josephson, Pippard and myself, as well as various other people who also habitually sat at the Mond tea and participated in the discussions of the next few weeks—very much puzzled by the meaning of the fact that the current depends on the phase.
4301:
4444:
3571:
2548:
4814:
3947:
1218:{\displaystyle {\frac {\partial }{\partial t}}({\sqrt {n_{A}}}e^{i\phi _{A}})={\dot {\sqrt {n_{A}}}}e^{i\phi _{A}}+{\sqrt {n_{A}}}(i{\dot {\phi }}_{A}e^{i\phi _{A}})=({\dot {\sqrt {n_{A}}}}+i{\sqrt {n_{A}}}{\dot {\phi }}_{A})e^{i\phi _{A}},}
2266:
5478:
3419:
1666:
233:
to claim the experimental observation of
Josephson's effect "Probable Observation of the Josephson Superconducting Tunneling Effect". These authors were awarded patents on the effects that were never enforced, but never challenged.
1501:
5701:
in its magnetic field when a current passes through it; However, in the case of
Josephson junction, no magnetic field is created by a supercurrent — the stored energy comes from the kinetic energy of the charge carriers instead.
2219:
6027:
2127:
4287:
When the current and
Josephson phase varies over time, the voltage drop across the junction will also vary accordingly; As shown in derivation below, the Josephson relations determine that this behavior can be modeled by a
3051:
156:
The DC Josephson effect had been seen in experiments prior to 1962, but had been attributed to "super-shorts" or breaches in the insulating barrier leading to the direct conduction of electrons between the superconductors.
6121:
5710:
The
Resistively Capacitance Shunted Junction (RCSJ) model, or simply shunted junction model, includes the effect of AC impedance of an actual Josephson junction on top of the two basic Josephson relations stated above.
2809:
3300:
5013:
4587:
3942:
4157:
3163:. The critical current of the Josephson junction depends on the properties of the superconductors, and can also be affected by environmental factors like temperature and externally applied magnetic field.
5570:
3475:
4894:
597:
533:
5751:
4306:
5688:
3599:
Typical I-V characteristic of a superconducting tunnel junction, a common kind of
Josephson junction. The scale of the vertical axis is 50 ÎĽA and that of the horizontal one is 1 mV. The bar at
3484:
218:, by then already Nobel Prize winner, was initially publicly skeptical of Josephson's theory in 1962, but came to accept it after further experiments and theoretical clarifications. See also:
2445:
1494:
422:
2980:
4424:{\displaystyle {\begin{aligned}{\frac {\partial I}{\partial \varphi }}&=I_{c}\cos \varphi ,\\{\frac {\partial \varphi }{\partial t}}&={\frac {2\pi }{\Phi _{0}}}V.\end{aligned}}}
5718:, the AC impedance of the junction can be represented by a capacitor and a shunt resistor, both parallel to the ideal Josephson Junction. The complete expression for the current drive
3219:
6778:, Anderson, Philip W. & Dayem, Aly H., "Superconductive device of varying dimension having a minimum dimension intermediate its electrodes", issued 1967-08-08
3309:
2259:
4957:
4567:{\displaystyle {\frac {\partial I}{\partial t}}={\frac {\partial I}{\partial \varphi }}{\frac {\partial \varphi }{\partial t}}=I_{c}\cos \varphi \cdot {\frac {2\pi }{\Phi _{0}}}V,}
3669:. This DC Josephson current is proportional to the sine of the Josephson phase (phase difference across the insulator, which stays constant over time), and may take values between
6899:
Fulton, T. A.; Gammel, P. L.; Bishop, D. J.; Dunkleberger, L. N.; Dolan, G. J. (1989). "Observation of
Combined Josephson and Charging Effects in Small Tunnel Junction Circuits".
5625:
2037:{\displaystyle 2{\dot {\sqrt {n_{A}}}}={\frac {1}{i\hbar }}(K{\sqrt {n_{B}}}e^{i\varphi }-K{\sqrt {n_{B}}}e^{-i\varphi })={\frac {K{\sqrt {n_{B}}}}{\hbar }}\cdot 2\sin \varphi .}
6087:
2908:
1862:
2729:{\displaystyle {\dot {n}}_{B}=-{\frac {2K{\sqrt {n_{A}n_{B}}}}{\hbar }}\sin \varphi ,\,{\dot {\phi }}_{B}={\frac {1}{\hbar }}(eV-K{\sqrt {\frac {n_{A}}{n_{B}}}}\cos \varphi ).}
1432:{\displaystyle ({\dot {\sqrt {n_{A}}}}+i{\sqrt {n_{A}}}{\dot {\phi }}_{A})e^{i\phi _{A}}={\frac {1}{i\hbar }}(eV{\sqrt {n_{A}}}e^{i\phi _{A}}+K{\sqrt {n_{B}}}e^{i\phi _{B}}).}
4908:
Based on the similarity of the
Josephson junction to a non-linear inductor, the energy stored in a Josephson junction when a supercurrent flows through it can be calculated.
4715:
5743:
3651:
2848:
6407:
6380:
5939:
5124:
5070:
2134:
3833:
468:
The Josephson effect can be calculated using the laws of quantum mechanics. A diagram of a single Josephson junction is shown at right. Assume that superconductor A has
6986:"The Feynman Lectures on Physics Vol. III Ch. 21: The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity, Section 21-9: The Josephson junction"
6057:
6113:
5376:
3864:
7378:
3762:
3697:
6353:
6326:
6299:
6084:
5876:
5097:
5043:
3793:
3724:
3141:
3114:
3085:
3623:
651:
117:, or S-I-S), a short section of non-superconducting metal (S-N-S), or a physical constriction that weakens the superconductivity at the point of contact (S-c-S).
4145:{\displaystyle V(t)={\frac {\hbar }{2e}}\omega (n+a\cos(\omega t)),{\text{ and }}I(t)=I_{c}\sum _{m=-\infty }^{\infty }J_{m}(a)\sin(\varphi _{0}+(n+m)\omega t),}
5896:
2868:
948:
625:
3232:
198:
After further review, they concluded that Josephson's results were valid. Josephson then submitted "Possible new effects in superconductive tunnelling" to
4279:
This means a Josephson junction can act like a perfect frequency-to-voltage converter, which is the theoretical basis for the Josephson voltage standard.
2431:{\displaystyle 2i{\sqrt {n_{A}}}{\dot {\phi }}_{A}={\frac {1}{i\hbar }}(2eV{\sqrt {n_{A}}}+K{\sqrt {n_{B}}}e^{i\varphi }+K{\sqrt {n_{B}}}e^{-i\varphi }),}
2049:
2989:
6264:{\displaystyle d'=d_{I}+\lambda _{1}\tanh \left({\frac {d_{1}}{2\lambda _{1}}}\right)+\lambda _{2}\tanh \left({\frac {d_{2}}{2\lambda _{2}}}\right),}
5947:
43:
1819:{\displaystyle {\dot {\sqrt {n_{A}}}}-i{\sqrt {n_{A}}}{\dot {\phi }}_{A}={\frac {1}{-i\hbar }}(eV{\sqrt {n_{A}}}+K{\sqrt {n_{B}}}e^{-i\varphi }).}
950:
is a characteristic of the junction. To solve the above equation, first calculate the time derivative of the order parameter in superconductor A:
8296:
3428:
1648:{\displaystyle {\dot {\sqrt {n_{A}}}}+i{\sqrt {n_{A}}}{\dot {\phi }}_{A}={\frac {1}{i\hbar }}(eV{\sqrt {n_{A}}}+K{\sqrt {n_{B}}}e^{i\varphi }),}
237:
Before Josephson's prediction, it was only known that single (i.e., non-paired) electrons can flow through an insulating barrier, by means of
7371:
2741:
7038:
Langenberg, D. N.; Scalapino, D. J.; Taylor, B. N.; Eck, R. E. (1966-04-01). "Microwave-induced D.C. voltages across Josephson junctions".
4699:{\displaystyle V={\frac {\Phi _{0}}{2\pi I_{c}\cos \varphi }}{\frac {\partial I}{\partial t}}=L(\varphi ){\frac {\partial I}{\partial t}}.}
4972:
160:
In 1962, Brian Josephson became interested into superconducting tunneling. He was then 23 years old and a second-year graduate student of
7966:
7271:
3869:
8029:
5362:
This shows that the change of energy in the Josephson junction depends only on the initial and final state of the junction and not the
113:(JJ). These consist of two or more superconductors coupled by a weak link. The weak link can be a thin insulating barrier (known as a
7908:
322:
7157:
McCumber, D. E. (1968-06-01). "Effect of ac Impedance on dc Voltage-Current Characteristics of Superconductor Weak-Link Junctions".
7364:
1450:
5572:
is a characteristic parameter of the Josephson junction, named the Josephson Energy. It is related to the Josephson Inductance by
5486:
3665:
The DC Josephson effect is a direct current crossing the insulator in the absence of any external electromagnetic field, owing to
4822:
3583:; Instead, this voltage comes from the kinetic energy of the carriers (i.e. the Cooper pairs). This phenomenon is also known as
6854:
98:, who predicted in 1962 the mathematical relationships for the current and voltage across the weak link. It is an example of a
7081:
Levinsen, M. T.; Chiao, R. Y.; Feldman, M. J.; Tucker, B. A. (1977-12-01). "An inverse ac Josephson effect voltage standard".
3175:
189:
Josephson and his colleagues were initially unsure about the validity of Josephson's calculations. Anderson later remembered:
7022:
5841:{\displaystyle I_{\text{ext}}=C_{J}{\frac {\operatorname {d} \!V}{\operatorname {d} \!t}}+I_{c}\sin \varphi +{\frac {V}{R}},}
538:
474:
8388:
8126:
8004:
5630:
94:
are placed in proximity, with some barrier or restriction between them. The effect is named after the British physicist
8236:
4578:
4270:{\displaystyle V_{\text{DC}}=n{\frac {\hbar }{2e}}\omega ,{\text{ and }}I_{\text{DC}}=I_{c}J_{-n}(a)\sin \varphi _{0}.}
8424:
8324:
7896:
6942:
Bouchiat, V.; Vion, D.; Joyez, P.; Esteve, D.; Devoret, M. H. (1998). "Quantum coherence with a single Cooper pair".
6720:
6462:
4911:
The supercurrent flowing through the junction is related to the Josephson phase by the current-phase relation (CPR):
427:
129:
61:
375:
is most precisely measured in terms of the Josephson constant and the von Klitzing constant which is related to the
8045:
390:
7201:
8241:
7959:
3866:
can induce quantized DC voltages across the Josephson junction, in which case the Josephson phase takes the form
2919:
445:
282:
114:
8024:
7994:
7344:
99:
8365:
8217:
8161:
8136:
7932:
7877:
7488:
6457:
4963:
3576:
2226:
464:
Diagram of a single Josephson junction. A and B represent superconductors, and C the weak link between them.
8267:
8196:
7423:
4917:
3566:{\displaystyle V={\frac {\Phi _{0}}{2\pi }}{\frac {\partial \varphi }{\partial t}}={\frac {d\Phi }{dt}}\,,}
5575:
8439:
8212:
8131:
2543:{\displaystyle {\dot {\phi }}_{A}=-{\frac {1}{\hbar }}(eV+K{\sqrt {\frac {n_{B}}{n_{A}}}}\cos \varphi ).}
4809:{\displaystyle L(\varphi )={\frac {\Phi _{0}}{2\pi I_{c}\cos \varphi }}={\frac {L_{J}}{\cos \varphi }}.}
2873:
1831:
219:
8429:
8319:
8314:
7999:
7952:
7668:
7577:
6452:
5363:
3666:
3657:
There are three main effects predicted by Josephson that follow directly from the Josephson equations:
469:
362:
349:
145:
6818:
Anderson, P. W.; Dayem, A. H. (1964). "Radio-frequency effects in superconducting thin film bridges".
8444:
8419:
8272:
8019:
7617:
7592:
6477:
6432:
3764:
across the junction, the phase will vary linearly with time and the current will be a sinusoidal AC (
6645:
5721:
3628:
2817:
8055:
7787:
7541:
7531:
7387:
6737:
6410:
3653:
is due to the finite value of the superconductor bandgap and not reproduced by the above equations.
658:
301:
7247:
6660:
6385:
6358:
5917:
5715:
5102:
5048:
8398:
8257:
8189:
8106:
7633:
5911:
3798:
278:
210:
169:
6712:
5906:
The Josephson penetration depth characterizes the typical length on which an externally applied
5473:{\displaystyle E(\varphi )=-{\frac {\Phi _{0}I_{c}}{2\pi }}\cos \varphi =-E_{J}\cos \varphi \,.}
654:
8309:
8282:
8262:
8184:
6035:
3414:{\displaystyle {\frac {\partial \varphi }{\partial t}}=2\pi ={\frac {2\pi }{\Phi _{0}}}V(t)\,.}
2812:
449:
270:
246:
7279:
6553:
8179:
7684:
7663:
7597:
6427:
3849:
3224:
385:
274:
3737:
3672:
3595:
8383:
8339:
7653:
7428:
7309:
7213:
7166:
7090:
7047:
7014:
6951:
6908:
6827:
6749:
6672:
6603:
6565:
6526:
6331:
6304:
6277:
6062:
5854:
5075:
5021:
4709:
This gives the expression for the kinetic inductance as a function of the Josephson Phase:
3771:
3702:
3119:
1441:
The phase difference of Ginzburg–Landau order parameters across the junction is called the
384:
digital electronics are based on shunted Josephson junctions. Junction switching emits one
7200:
Chakravarty, Sudip; Ingold, Gert-Ludwig; Kivelson, Steven; Zimanyi, Gergely (1988-03-01).
7124:
Devoret, M.; Wallraff, A.; Martinis, J. (2004). "Superconducting Qubits: A Short Review".
6794:
3090:
3061:
39:
8:
7607:
7587:
7572:
7521:
6447:
4896:
is a characteristic parameter of the Josephson junction, named the Josephson Inductance.
3765:
3602:
630:
439:
376:
7313:
7217:
7170:
7094:
7051:
6955:
6912:
6831:
6753:
6676:
6607:
6569:
6530:
6093:
607:
in the two superconductors. If the electric potential difference across the junction is
293:
Josephson junction where the weak link comprises a superconducting wire measuring a few
8370:
8121:
8081:
7754:
7744:
7582:
7493:
7125:
6967:
6705:
6581:
6442:
5881:
4289:
3835:. This means a Josephson junction can act as a perfect voltage-to-frequency converter.
3584:
3167:
2853:
933:
610:
173:
7202:"Quantum statistical mechanics of an array of resistively shunted Josephson junctions"
6963:
8146:
7975:
7915:
7862:
7827:
7734:
7658:
7340:
7229:
7182:
7106:
7063:
7059:
7018:
6971:
6924:
6716:
6538:
6488:
6472:
3844:
2214:{\displaystyle {\dot {n}}_{A}={\frac {2K{\sqrt {n_{A}n_{B}}}}{\hbar }}\sin \varphi .}
1658:
372:
262:
238:
6862:
6585:
8434:
8355:
8329:
8076:
8009:
7832:
7724:
7704:
7699:
7694:
7689:
7526:
7483:
7448:
7418:
7317:
7221:
7174:
7098:
7055:
6959:
6916:
6835:
6757:
6680:
6611:
6573:
6534:
6493:
6467:
5698:
353:
165:
6985:
6775:
109:, that flows continuously without any voltage applied, across a device known as a
8378:
8111:
7857:
7812:
7478:
7395:
7144:
6437:
5126:. The energy increase in the junction is equal to the work done on the junction:
3580:
2122:{\displaystyle {\dot {\sqrt {n_{A}}}}={\frac {{\dot {n}}_{A}}{2{\sqrt {n_{A}}}}}}
366:
337:
200:
121:
95:
91:
7300:
Weihnacht, M. (1969). "Influence of Film Thickness on D. C. Josephson Current".
6920:
3579:. But note that this voltage does not come from magnetic energy, since there is
3046:{\displaystyle {\frac {\partial \varphi }{\partial t}}={\frac {2eV(t)}{\hbar }}}
8116:
8060:
8050:
8014:
7920:
7867:
7749:
7638:
6839:
6761:
6517:
Josephson, B. D. (1962). "Possible new effects in superconductive tunnelling".
6022:{\displaystyle \lambda _{J}={\sqrt {\frac {\Phi _{0}}{2\pi \mu _{0}d'j_{c}}}},}
5907:
5367:
305:
6684:
6615:
6577:
8413:
7792:
7774:
7759:
7739:
7643:
7612:
7443:
7321:
7225:
7186:
7110:
7067:
600:
161:
460:
257:
186:
Falicov, and Phillips about the superconductor-barrier-normal metal system.
8151:
8141:
8096:
8091:
7729:
7551:
7453:
7356:
6928:
3116:
are the voltage across and the current through the Josephson junction, and
315:
215:
182:
106:
7233:
8277:
8086:
7849:
7567:
7536:
7516:
7463:
7130:
3625:
represents the DC Josephson effect, while the current at large values of
604:
242:
7339:(6. ed.). TĂĽbingen: Wiley-VCH Verlag GmbH&Co.KGaA. p. 67.
7989:
7764:
7602:
7438:
6483:
6414:
4435:
2804:{\displaystyle {\dot {\varphi }}={\dot {\phi }}_{B}-{\dot {\phi }}_{A}}
435:
326:
294:
7178:
6594:
Josephson, B. D. (1974). "The Discovery of Tunnelling Supercurrents".
3295:{\displaystyle \Phi _{0}={\frac {h}{2e}}=2\pi {\frac {\hbar }{2e}}\,.}
314:, or superconducting quantum interference devices, are very sensitive
241:. Josephson was the first to predict the tunneling of superconducting
7822:
7648:
7433:
341:
333:
290:
226:
177:
7944:
7102:
5008:{\displaystyle V=\operatorname {d} \!\Phi /\operatorname {d} \!t\,.}
3304:
The superconducting phase evolution equation can be reexpressed as:
8304:
5694:
653:, since each Cooper pair has twice the charge of one electron. The
369:
materials and called "superconducting single-electron transistors".
356:
definition of frequency and gives the standard representation of a
3937:{\displaystyle \varphi (t)=\varphi _{0}+n\omega t+a\sin(\omega t)}
7872:
7839:
7817:
7797:
345:
7199:
627:, then the energy difference between the two superconductors is
7807:
7802:
7408:
7147:, Introduction to superconductivity, Courier Corporation, 1986.
6659:
Cohen, M. H.; Falicov, L. M.; Phillips, J. C. (15 April 1962).
6301:
is the thickness of the Josephson barrier (usually insulator),
6115:
characterizes the inductance of the superconducting electrodes
431:
74:
6898:
5878:– effective capacitance, and the third is normal current with
8360:
8334:
7782:
7403:
4962:
The superconducting phase evolution equation is analogous to
311:
125:
7037:
6413:. The Josephson penetration depth usually ranges from a few
5565:{\displaystyle E_{J}=|E(0)|={\frac {\Phi _{0}I_{c}}{2\pi }}}
5366:. Therefore, the energy stored in a Josephson junction is a
8393:
6417:
to several mm if the critical current density is very low.
3944:, and the voltage and current across the junction will be:
3470:{\displaystyle \Phi =\Phi _{0}{\frac {\varphi }{2\pi }}\,,}
381:
357:
172:. That year, Josephson took a many-body theory course with
141:
137:
133:
79:
7080:
6646:"The Discovery of Tunneling Supercurrents (Nobel Lecture)"
4889:{\displaystyle L_{J}=L(0)={\frac {\Phi _{0}}{2\pi I_{c}}}}
7413:
1496:
The Schrödinger equation can therefore be rewritten as:
7123:
6941:
6355:
are the thicknesses of superconducting electrodes, and
2223:
Now, subtract the two conjugate equations to eliminate
592:{\displaystyle \psi _{B}={\sqrt {n_{B}}}e^{i\phi _{B}}}
528:{\displaystyle \psi _{A}={\sqrt {n_{A}}}e^{i\phi _{A}}}
1828:
Add the two conjugate equations together to eliminate
832:
787:
696:
394:
6738:"Probable Observation of the Josephson Tunnel Effect"
6388:
6361:
6334:
6307:
6280:
6124:
6096:
6065:
6038:
5950:
5920:
5884:
5857:
5754:
5724:
5633:
5578:
5489:
5379:
5135:
5105:
5078:
5051:
5024:
4975:
4920:
4825:
4718:
4590:
4447:
4304:
4160:
3950:
3872:
3852:
3801:
3774:
3740:
3705:
3675:
3631:
3605:
3487:
3431:
3312:
3235:
3178:
3122:
3093:
3064:
2992:
2922:
2876:
2856:
2820:
2744:
2560:
2448:
2269:
2229:
2137:
2052:
1872:
1834:
1669:
1504:
1453:
1235:
958:
936:
669:
633:
613:
541:
477:
424:. Its presence and absence represents binary 1 and 0.
393:
6658:
6512:
6510:
2552:
Similarly, for superconductor B we can derive that:
105:
The Josephson effect produces a current, known as a
229:colleague John Rowell submitted the first paper to
120:Josephson junctions have important applications in
34:
may be too technical for most readers to understand
6704:
6401:
6374:
6347:
6320:
6293:
6263:
6107:
6078:
6051:
6021:
5941:and is given by the following expression (in SI):
5933:
5890:
5870:
5851:where the first term is displacement current with
5840:
5737:
5683:{\displaystyle E(\varphi )=E_{J}(1-\cos \varphi )}
5682:
5619:
5564:
5472:
5351:
5118:
5091:
5064:
5037:
5007:
4951:
4888:
4808:
4698:
4566:
4423:
4269:
4144:
3936:
3858:
3838:
3827:
3787:
3756:
3718:
3691:
3645:
3617:
3565:
3469:
3413:
3294:
3213:
3135:
3108:
3079:
3045:
2974:
2902:
2862:
2842:
2803:
2728:
2542:
2430:
2253:
2213:
2121:
2036:
1856:
1818:
1647:
1488:
1431:
1217:
942:
920:
645:
619:
591:
527:
416:
6707:True Genius: The Life and Science of John Bardeen
6507:
5793:
5784:
5257:
5199:
5169:
4997:
4985:
4438:to calculate the time derivative of the current:
249:in 1973. John Bardeen was one of the nominators.
8411:
7011:Physics and Applications of the Josephson Effect
6736:Anderson, P. W.; Rowell, J. M. (15 March 1963).
2738:Noting that the evolution of Josephson phase is
438:or other schemes where the phase and charge are
321:Superfluid helium quantum interference devices (
220:John Bardeen § Josephson Effect controversy
146:an array of 20,208 Josephson junctions in series
115:superconductor–insulator–superconductor junction
6632:Sync: The Emerging Science of Spontaneous Order
78:Josephson junction array chip developed by the
6735:
6702:
5901:
4577:Rearrange the above result in the form of the
1227:and therefore the Schrödinger equation gives:
80:National Institute of Standards and Technology
7960:
7372:
7334:
7008:
6855:"SQUIDs: A Technical Report – Part 3: SQUIDs"
6817:
6774:
1489:{\displaystyle \varphi =\phi _{B}-\phi _{A}.}
417:{\displaystyle \scriptstyle {\frac {1}{2e}}h}
208:was chosen instead of the better established
7386:
6698:
6696:
6694:
214:due to their uncertainty about the results.
6554:"The discovery of tunnelling supercurrents"
5627:. An alternative but equivalent definition
2975:{\displaystyle I(t)=I_{c}\sin(\varphi (t))}
7967:
7953:
7462:
7379:
7365:
7335:Buckel, Werner; Kleiner, Reinhold (2004).
3729:
3660:
455:
7299:
7129:
6703:Daitch, Vicki; Hoddeson, Lillian (2002).
6691:
6644:Josephson, Brian D. (December 12, 1973).
6643:
6593:
6551:
6516:
5466:
5345:
5001:
3559:
3479:then the voltage across the junction is:
3463:
3407:
3288:
3207:
3143:is a parameter of the junction named the
2637:
62:Learn how and when to remove this message
46:, without removing the technical details.
7156:
5898:– effective resistance of the junction.
3594:
3581:no magnetic field in the superconductors
3214:{\displaystyle K_{J}={\frac {2e}{h}}\,,}
3161:superconducting phase evolution equation
459:
269:Types of Josephson junction include the
256:
245:. For this work, Josephson received the
73:
4282:
8412:
7002:
6885:Sato, Y.; Packard, R. (October 2012),
2254:{\displaystyle {\dot {\sqrt {n_{A}}}}}
7974:
7948:
7360:
4952:{\displaystyle I=I_{c}\sin \varphi .}
3590:
318:that operate via the Josephson effect
90:is a phenomenon that occurs when two
44:make it understandable to non-experts
7903:
6852:
5620:{\displaystyle E_{J}=L_{J}I_{c}^{2}}
4295:Rewrite the Josephson relations as:
18:
7927:
4903:
13:
6545:
6040:
5968:
5790:
5781:
5532:
5402:
5333:
5303:
5264:
5254:
5200:
5196:
5166:
5136:
4994:
4986:
4982:
4857:
4737:
4684:
4676:
4649:
4641:
4600:
4547:
4502:
4494:
4482:
4474:
4459:
4451:
4400:
4373:
4365:
4320:
4312:
4069:
4064:
3545:
3527:
3519:
3497:
3439:
3432:
3384:
3324:
3316:
3237:
3004:
2996:
2903:{\displaystyle n_{A}\approx n_{B}}
1857:{\displaystyle {\dot {\phi }}_{A}}
965:
961:
682:
678:
599:, which can be interpreted as the
225:In January 1963, Anderson and his
14:
8456:
6964:10.1238/Physica.Topical.076a00165
6887:Superfluid helium interferometers
6853:Dawe, Richard (28 October 1998).
6795:"The Nobel Prize in Physics 1973"
6463:Macroscopic quantum self-trapping
5705:
5099:, the Josephson phase evolved to
3155:, and equation (2) is called the
3038:
2665:
2620:
2479:
2321:
2194:
2011:
1909:
1745:
1577:
1334:
673:
428:Superconducting quantum computing
7926:
7914:
7902:
7891:
7890:
7009:Barone, A.; Paterno, G. (1982).
3843:Microwave radiation of a single
3153:weak-link current-phase relation
2910:, the above solution yields the
204:in June 1962. The newer journal
23:
7328:
7293:
7264:
7240:
7193:
7150:
7138:
7117:
7074:
7031:
6978:
6935:
6892:
6879:
6846:
6811:
3839:The inverse AC Josephson effect
470:Ginzburg–Landau order parameter
446:Superconducting tunnel junction
283:superconducting tunnel junction
252:
6787:
6768:
6729:
6711:. Joseph Henry Press. p.
6652:
6637:
6624:
6059:is the magnetic flux quantum,
5738:{\displaystyle I_{\text{ext}}}
5693:Again, note that a non-linear
5677:
5659:
5643:
5637:
5521:
5517:
5511:
5504:
5389:
5383:
4848:
4842:
4728:
4722:
4670:
4664:
4579:current–voltage characteristic
4245:
4239:
4136:
4127:
4115:
4099:
4090:
4084:
4034:
4028:
4014:
4011:
4002:
3984:
3960:
3954:
3931:
3922:
3882:
3876:
3646:{\displaystyle \left|V\right|}
3404:
3398:
3367:
3364:
3358:
3342:
3103:
3097:
3074:
3068:
3034:
3028:
2969:
2966:
2960:
2954:
2932:
2926:
2843:{\displaystyle {\dot {n}}_{A}}
2720:
2670:
2534:
2484:
2422:
2327:
1984:
1915:
1810:
1751:
1639:
1583:
1423:
1340:
1299:
1236:
1189:
1126:
1120:
1075:
1011:
974:
100:macroscopic quantum phenomenon
1:
7489:Spontaneous symmetry breaking
7252:hyperphysics.phy-astr.gsu.edu
6500:
6458:Macroscopic quantum phenomena
6088:critical supercurrent density
3147:. Equation (1) is called the
7060:10.1016/0031-9163(66)91114-0
6539:10.1016/0031-9163(62)91369-0
6402:{\displaystyle \lambda _{2}}
6375:{\displaystyle \lambda _{1}}
5934:{\displaystyle \lambda _{J}}
5119:{\displaystyle \varphi _{2}}
5065:{\displaystyle \varphi _{1}}
4292:named Josephson Inductance.
2986:
2916:
336:, the Josephson effect is a
7:
6990:feynmanlectures.caltech.edu
6921:10.1103/PhysRevLett.63.1307
6661:"Superconductive Tunneling"
6420:
5914:. It is usually denoted as
5902:Josephson penetration depth
5370:, which can be defined as:
3828:{\displaystyle K_{J}V_{DC}}
2850:is proportional to current
2811:and the time derivative of
430:uses Josephon junctions as
363:Single-electron transistors
329:helium analog of a dc-SQUID
122:quantum-mechanical circuits
16:Quantum physical phenomenon
10:
8461:
8297:Technological applications
7669:Spin gapless semiconductor
7578:Nearly free electron model
7159:Journal of Applied Physics
6840:10.1103/PhysRevLett.13.195
6762:10.1103/PhysRevLett.10.230
3577:Faraday's law of induction
350:Josephson voltage standard
151:
8348:
8295:
8250:
8226:
8205:
8169:
8160:
8069:
8039:Characteristic parameters
8038:
7982:
7886:
7848:
7773:
7717:
7677:
7626:
7618:Density functional theory
7593:electronic band structure
7560:
7509:
7502:
7471:
7460:
7394:
6685:10.1103/PhysRevLett.8.316
6578:10.1103/RevModPhys.46.251
6558:Reviews of Modern Physics
6552:Josephson, B. D. (1974).
6478:Rapid single flux quantum
6411:London penetration depths
6052:{\displaystyle \Phi _{0}}
5045:, the Josephson phase is
3575:which is very similar to
3157:second Josephson relation
308:for a device's complexity
136:digital electronics. The
8425:Condensed matter physics
8056:London penetration depth
7788:Bogoliubov quasiparticle
7532:Quantum spin Hall effect
7424:Bose–Einstein condensate
7388:Condensed matter physics
7322:10.1002/pssb.19690320259
7226:10.1103/PhysRevB.37.3283
3149:first Josephson relation
659:two-state quantum system
302:Josephson junction count
265:for a Josephson junction
8349:List of superconductors
8227:By critical temperature
7302:Physica Status Solidi B
7276:phelafel.technion.ac.il
7248:"AC Thevenin's Theorem"
7083:Applied Physics Letters
6901:Physical Review Letters
6889:, Physics Today, p. 31.
6820:Physical Review Letters
6742:Physical Review Letters
6665:Physical Review Letters
6616:10.1051/epn/19740503001
5912:long Josephson junction
4154:The DC components are:
3859:{\displaystyle \omega }
3730:The AC Josephson effect
3661:The DC Josephson effect
3223:and its inverse is the
535:, and superconductor B
456:The Josephson equations
450:superconducting cameras
279:long Josephson junction
277:is a special example),
231:Physical Review Letters
211:Physical Review Letters
170:University of Cambridge
7272:"Dynamics of RF SQUID"
6453:Ginzburg–Landau theory
6403:
6376:
6349:
6322:
6295:
6265:
6109:
6080:
6053:
6023:
5935:
5892:
5872:
5842:
5739:
5695:magnetic coil inductor
5684:
5621:
5566:
5474:
5353:
5120:
5093:
5066:
5039:
5009:
4953:
4890:
4810:
4700:
4568:
4425:
4271:
4146:
4073:
3938:
3860:
3829:
3789:
3758:
3757:{\displaystyle V_{DC}}
3720:
3693:
3692:{\displaystyle -I_{c}}
3654:
3647:
3619:
3567:
3471:
3415:
3296:
3215:
3137:
3110:
3081:
3047:
2976:
2904:
2864:
2844:
2813:charge carrier density
2805:
2730:
2544:
2432:
2255:
2215:
2123:
2038:
1858:
1820:
1649:
1490:
1433:
1219:
944:
922:
647:
621:
593:
529:
465:
448:detectors are used in
418:
289:A "Dayem bridge" is a
285:. Other uses include:
266:
247:Nobel Prize in Physics
196:
130:superconducting qubits
83:
7995:Bean's critical state
7664:Topological insulator
7598:Anderson localization
7015:John Wiley & Sons
6428:Pi Josephson junction
6404:
6377:
6350:
6348:{\displaystyle d_{2}}
6323:
6321:{\displaystyle d_{1}}
6296:
6294:{\displaystyle d_{I}}
6266:
6110:
6081:
6079:{\displaystyle j_{c}}
6054:
6024:
5936:
5893:
5873:
5871:{\displaystyle C_{J}}
5843:
5740:
5685:
5622:
5567:
5475:
5354:
5121:
5094:
5092:{\displaystyle t_{2}}
5067:
5040:
5038:{\displaystyle t_{1}}
5010:
4954:
4891:
4811:
4701:
4569:
4426:
4272:
4147:
4050:
3939:
3861:
3830:
3790:
3788:{\displaystyle I_{c}}
3759:
3734:With a fixed voltage
3721:
3719:{\displaystyle I_{c}}
3694:
3648:
3620:
3598:
3568:
3472:
3416:
3297:
3225:magnetic flux quantum
3216:
3138:
3136:{\displaystyle I_{c}}
3111:
3082:
3048:
2977:
2905:
2865:
2845:
2806:
2731:
2545:
2433:
2256:
2216:
2124:
2039:
1859:
1821:
1650:
1491:
1434:
1220:
945:
923:
648:
622:
594:
530:
463:
419:
386:magnetic flux quantum
260:
191:
77:
8170:By magnetic response
7542:Aharonov–Bohm effect
7429:Fermionic condensate
6433:φ Josephson junction
6386:
6359:
6332:
6305:
6278:
6122:
6094:
6063:
6036:
5948:
5918:
5910:penetrates into the
5882:
5855:
5752:
5722:
5690:is also often used.
5631:
5576:
5487:
5377:
5133:
5103:
5076:
5049:
5022:
5018:Assume that at time
4973:
4918:
4823:
4716:
4588:
4445:
4302:
4283:Josephson inductance
4158:
3948:
3870:
3850:
3799:
3772:
3738:
3703:
3673:
3629:
3603:
3485:
3429:
3310:
3233:
3176:
3120:
3109:{\displaystyle I(t)}
3091:
3080:{\displaystyle V(t)}
3062:
2990:
2920:
2874:
2854:
2818:
2742:
2558:
2446:
2267:
2227:
2135:
2050:
1870:
1832:
1667:
1502:
1451:
1233:
956:
934:
667:
655:Schrödinger equation
631:
611:
539:
475:
391:
365:are often made from
275:Ď€ Josephson junction
271:φ Josephson junction
8122:persistent currents
8107:Little–Parks effect
7933:Physics WikiProject
7608:tight binding model
7588:Fermi liquid theory
7573:Free electron model
7522:Quantum Hall effect
7503:Electrons in solids
7314:1969PSSBR..32..169W
7218:1988PhRvB..37.3283C
7171:1968JAP....39.3113M
7095:1977ApPhL..31..776L
7052:1966PhL....20..563L
6956:1998PhST...76..165B
6913:1989PhRvL..63.1307F
6832:1964PhRvL..13..195A
6754:1963PhRvL..10..230A
6677:1962PhRvL...8..316C
6608:1974ENews...5c...1J
6570:1974RvMP...46..251J
6531:1962PhL.....1..251J
6448:Fractional vortices
5616:
5234:
5192:
5159:
3845:(angular) frequency
3766:alternating current
3618:{\displaystyle V=0}
2912:Josephson equations
930:where the constant
646:{\displaystyle 2eV}
440:conjugate variables
377:quantum Hall effect
340:conversion between
8440:Mesoscopic physics
8082:Andreev reflection
8077:Abrikosov vortices
7494:Critical phenomena
6443:Andreev reflection
6399:
6372:
6345:
6318:
6291:
6261:
6108:{\displaystyle d'}
6105:
6076:
6049:
6019:
5931:
5888:
5868:
5838:
5735:
5716:Thévenin's theorem
5680:
5617:
5602:
5562:
5470:
5349:
5206:
5178:
5145:
5116:
5089:
5072:; At a later time
5062:
5035:
5005:
4949:
4886:
4806:
4696:
4564:
4421:
4419:
4290:kinetic inductance
4267:
4142:
3934:
3856:
3825:
3785:
3754:
3716:
3689:
3655:
3643:
3615:
3591:Three main effects
3585:kinetic inductance
3563:
3467:
3411:
3292:
3211:
3168:Josephson constant
3133:
3106:
3077:
3043:
2972:
2900:
2860:
2840:
2801:
2726:
2540:
2428:
2251:
2211:
2119:
2034:
1854:
1816:
1645:
1486:
1429:
1215:
940:
918:
909:
821:
773:
643:
617:
589:
525:
466:
414:
413:
267:
174:Philip W. Anderson
111:Josephson junction
84:
82:as a standard volt
8430:Superconductivity
8407:
8406:
8325:quantum computing
8291:
8290:
8147:superdiamagnetism
7976:Superconductivity
7942:
7941:
7828:Exciton-polariton
7713:
7712:
7685:Thermoelectricity
7206:Physical Review B
7179:10.1063/1.1656743
7024:978-0-471-01469-0
6907:(12): 1307–1310.
6634:, Hyperion, 2003.
6630:Steven Strogatz,
6489:Zero-point energy
6473:Quantum gyroscope
6252:
6196:
6014:
6013:
5891:{\displaystyle R}
5833:
5798:
5762:
5732:
5560:
5430:
5331:
5286:
4884:
4801:
4773:
4691:
4656:
4636:
4556:
4509:
4489:
4466:
4409:
4380:
4327:
4210:
4201:
4190:
4168:
4023:
3979:
3768:) with amplitude
3557:
3534:
3514:
3461:
3393:
3331:
3286:
3262:
3205:
3041:
3011:
2863:{\displaystyle I}
2831:
2792:
2770:
2754:
2709:
2708:
2668:
2648:
2623:
2617:
2571:
2523:
2522:
2482:
2459:
2404:
2371:
2351:
2325:
2300:
2288:
2248:
2244:
2197:
2191:
2148:
2117:
2114:
2089:
2071:
2067:
2014:
2008:
1966:
1933:
1913:
1894:
1890:
1845:
1792:
1772:
1749:
1721:
1709:
1688:
1684:
1659:complex conjugate
1624:
1604:
1581:
1556:
1544:
1523:
1519:
1401:
1361:
1338:
1290:
1278:
1257:
1253:
1180:
1168:
1147:
1143:
1091:
1073:
1035:
1031:
989:
972:
943:{\displaystyle K}
885:
847:
749:
711:
689:
620:{\displaystyle V}
567:
503:
408:
373:Elementary charge
263:electrical symbol
239:quantum tunneling
140:standard for one
72:
71:
64:
8452:
8445:Energy (physics)
8420:Josephson effect
8356:bilayer graphene
8330:Rutherford cable
8242:room temperature
8237:high temperature
8167:
8166:
8127:proximity effect
8102:Josephson effect
8046:coherence length
7969:
7962:
7955:
7946:
7945:
7930:
7929:
7918:
7906:
7905:
7894:
7893:
7833:Phonon polariton
7725:Amorphous magnet
7705:Electrostriction
7700:Flexoelectricity
7695:Ferroelectricity
7690:Piezoelectricity
7547:Josephson effect
7527:Spin Hall effect
7507:
7506:
7484:Phase transition
7466:
7449:Luttinger liquid
7396:States of matter
7381:
7374:
7367:
7358:
7357:
7351:
7350:
7332:
7326:
7325:
7297:
7291:
7290:
7288:
7287:
7278:. Archived from
7268:
7262:
7261:
7259:
7258:
7244:
7238:
7237:
7212:(7): 3283–3294.
7197:
7191:
7190:
7165:(7): 3113–3118.
7154:
7148:
7142:
7136:
7135:
7133:
7131:cond-mat/0411174
7121:
7115:
7114:
7078:
7072:
7071:
7035:
7029:
7028:
7006:
7000:
6999:
6997:
6996:
6982:
6976:
6975:
6939:
6933:
6932:
6896:
6890:
6883:
6877:
6876:
6874:
6873:
6867:
6861:. Archived from
6850:
6844:
6843:
6815:
6809:
6808:
6806:
6805:
6791:
6785:
6784:
6783:
6779:
6772:
6766:
6765:
6733:
6727:
6726:
6710:
6700:
6689:
6688:
6656:
6650:
6649:
6641:
6635:
6628:
6622:
6619:
6596:Europhysics News
6589:
6549:
6543:
6542:
6514:
6494:Josephson vortex
6468:Quantum computer
6408:
6406:
6405:
6400:
6398:
6397:
6381:
6379:
6378:
6373:
6371:
6370:
6354:
6352:
6351:
6346:
6344:
6343:
6327:
6325:
6324:
6319:
6317:
6316:
6300:
6298:
6297:
6292:
6290:
6289:
6270:
6268:
6267:
6262:
6257:
6253:
6251:
6250:
6249:
6236:
6235:
6226:
6214:
6213:
6201:
6197:
6195:
6194:
6193:
6180:
6179:
6170:
6158:
6157:
6145:
6144:
6132:
6114:
6112:
6111:
6106:
6104:
6085:
6083:
6082:
6077:
6075:
6074:
6058:
6056:
6055:
6050:
6048:
6047:
6028:
6026:
6025:
6020:
6015:
6012:
6011:
6010:
6001:
5993:
5992:
5976:
5975:
5966:
5965:
5960:
5959:
5940:
5938:
5937:
5932:
5930:
5929:
5897:
5895:
5894:
5889:
5877:
5875:
5874:
5869:
5867:
5866:
5847:
5845:
5844:
5839:
5834:
5826:
5812:
5811:
5799:
5797:
5788:
5779:
5777:
5776:
5764:
5763:
5760:
5744:
5742:
5741:
5736:
5734:
5733:
5730:
5699:potential energy
5689:
5687:
5686:
5681:
5658:
5657:
5626:
5624:
5623:
5618:
5615:
5610:
5601:
5600:
5588:
5587:
5571:
5569:
5568:
5563:
5561:
5559:
5551:
5550:
5549:
5540:
5539:
5529:
5524:
5507:
5499:
5498:
5479:
5477:
5476:
5471:
5456:
5455:
5431:
5429:
5421:
5420:
5419:
5410:
5409:
5399:
5358:
5356:
5355:
5350:
5332:
5330:
5322:
5321:
5320:
5311:
5310:
5300:
5292:
5288:
5287:
5285:
5274:
5272:
5271:
5244:
5243:
5233:
5232:
5231:
5221:
5220:
5219:
5191:
5186:
5174:
5158:
5153:
5125:
5123:
5122:
5117:
5115:
5114:
5098:
5096:
5095:
5090:
5088:
5087:
5071:
5069:
5068:
5063:
5061:
5060:
5044:
5042:
5041:
5036:
5034:
5033:
5014:
5012:
5011:
5006:
4993:
4958:
4956:
4955:
4950:
4936:
4935:
4904:Josephson energy
4895:
4893:
4892:
4887:
4885:
4883:
4882:
4881:
4865:
4864:
4855:
4835:
4834:
4815:
4813:
4812:
4807:
4802:
4800:
4789:
4788:
4779:
4774:
4772:
4762:
4761:
4745:
4744:
4735:
4705:
4703:
4702:
4697:
4692:
4690:
4682:
4674:
4657:
4655:
4647:
4639:
4637:
4635:
4625:
4624:
4608:
4607:
4598:
4581:of an inductor:
4573:
4571:
4570:
4565:
4557:
4555:
4554:
4545:
4537:
4523:
4522:
4510:
4508:
4500:
4492:
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4488:
4480:
4472:
4467:
4465:
4457:
4449:
4430:
4428:
4427:
4422:
4420:
4410:
4408:
4407:
4398:
4390:
4381:
4379:
4371:
4363:
4345:
4344:
4328:
4326:
4318:
4310:
4276:
4274:
4273:
4268:
4263:
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4238:
4237:
4225:
4224:
4212:
4211:
4208:
4202:
4199:
4191:
4189:
4178:
4170:
4169:
4166:
4151:
4149:
4148:
4143:
4111:
4110:
4083:
4082:
4072:
4067:
4049:
4048:
4024:
4021:
3980:
3978:
3967:
3943:
3941:
3940:
3935:
3897:
3896:
3865:
3863:
3862:
3857:
3834:
3832:
3831:
3826:
3824:
3823:
3811:
3810:
3794:
3792:
3791:
3786:
3784:
3783:
3763:
3761:
3760:
3755:
3753:
3752:
3725:
3723:
3722:
3717:
3715:
3714:
3698:
3696:
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3652:
3650:
3649:
3644:
3642:
3624:
3622:
3621:
3616:
3572:
3570:
3569:
3564:
3558:
3556:
3548:
3540:
3535:
3533:
3525:
3517:
3515:
3513:
3505:
3504:
3495:
3476:
3474:
3473:
3468:
3462:
3460:
3449:
3447:
3446:
3420:
3418:
3417:
3412:
3394:
3392:
3391:
3382:
3374:
3354:
3353:
3332:
3330:
3322:
3314:
3301:
3299:
3298:
3293:
3287:
3285:
3274:
3263:
3261:
3250:
3245:
3244:
3220:
3218:
3217:
3212:
3206:
3201:
3193:
3188:
3187:
3145:critical current
3142:
3140:
3139:
3134:
3132:
3131:
3115:
3113:
3112:
3107:
3086:
3084:
3083:
3078:
3052:
3050:
3049:
3044:
3042:
3037:
3017:
3012:
3010:
3002:
2994:
2981:
2979:
2978:
2973:
2947:
2946:
2909:
2907:
2906:
2901:
2899:
2898:
2886:
2885:
2869:
2867:
2866:
2861:
2849:
2847:
2846:
2841:
2839:
2838:
2833:
2832:
2824:
2810:
2808:
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2800:
2799:
2794:
2793:
2785:
2778:
2777:
2772:
2771:
2763:
2756:
2755:
2747:
2735:
2733:
2732:
2727:
2710:
2707:
2706:
2697:
2696:
2687:
2686:
2669:
2661:
2656:
2655:
2650:
2649:
2641:
2624:
2619:
2618:
2616:
2615:
2606:
2605:
2596:
2587:
2579:
2578:
2573:
2572:
2564:
2549:
2547:
2546:
2541:
2524:
2521:
2520:
2511:
2510:
2501:
2500:
2483:
2475:
2467:
2466:
2461:
2460:
2452:
2437:
2435:
2434:
2429:
2421:
2420:
2405:
2403:
2402:
2393:
2385:
2384:
2372:
2370:
2369:
2360:
2352:
2350:
2349:
2340:
2326:
2324:
2313:
2308:
2307:
2302:
2301:
2293:
2289:
2287:
2286:
2277:
2260:
2258:
2257:
2252:
2250:
2249:
2243:
2242:
2233:
2232:
2220:
2218:
2217:
2212:
2198:
2193:
2192:
2190:
2189:
2180:
2179:
2170:
2161:
2156:
2155:
2150:
2149:
2141:
2128:
2126:
2125:
2120:
2118:
2116:
2115:
2113:
2112:
2103:
2097:
2096:
2091:
2090:
2082:
2078:
2073:
2072:
2066:
2065:
2056:
2055:
2043:
2041:
2040:
2035:
2015:
2010:
2009:
2007:
2006:
1997:
1991:
1983:
1982:
1967:
1965:
1964:
1955:
1947:
1946:
1934:
1932:
1931:
1922:
1914:
1912:
1901:
1896:
1895:
1889:
1888:
1879:
1878:
1863:
1861:
1860:
1855:
1853:
1852:
1847:
1846:
1838:
1825:
1823:
1822:
1817:
1809:
1808:
1793:
1791:
1790:
1781:
1773:
1771:
1770:
1761:
1750:
1748:
1734:
1729:
1728:
1723:
1722:
1714:
1710:
1708:
1707:
1698:
1690:
1689:
1683:
1682:
1673:
1672:
1654:
1652:
1651:
1646:
1638:
1637:
1625:
1623:
1622:
1613:
1605:
1603:
1602:
1593:
1582:
1580:
1569:
1564:
1563:
1558:
1557:
1549:
1545:
1543:
1542:
1533:
1525:
1524:
1518:
1517:
1508:
1507:
1495:
1493:
1492:
1487:
1482:
1481:
1469:
1468:
1438:
1436:
1435:
1430:
1422:
1421:
1420:
1419:
1402:
1400:
1399:
1390:
1382:
1381:
1380:
1379:
1362:
1360:
1359:
1350:
1339:
1337:
1326:
1321:
1320:
1319:
1318:
1298:
1297:
1292:
1291:
1283:
1279:
1277:
1276:
1267:
1259:
1258:
1252:
1251:
1242:
1241:
1224:
1222:
1221:
1216:
1211:
1210:
1209:
1208:
1188:
1187:
1182:
1181:
1173:
1169:
1167:
1166:
1157:
1149:
1148:
1142:
1141:
1132:
1131:
1119:
1118:
1117:
1116:
1099:
1098:
1093:
1092:
1084:
1074:
1072:
1071:
1062:
1057:
1056:
1055:
1054:
1037:
1036:
1030:
1029:
1020:
1019:
1010:
1009:
1008:
1007:
990:
988:
987:
978:
973:
971:
960:
949:
947:
946:
941:
927:
925:
924:
919:
914:
913:
906:
905:
904:
903:
886:
884:
883:
874:
868:
867:
866:
865:
848:
846:
845:
836:
826:
825:
778:
777:
770:
769:
768:
767:
750:
748:
747:
738:
732:
731:
730:
729:
712:
710:
709:
700:
690:
688:
677:
652:
650:
649:
644:
626:
624:
623:
618:
598:
596:
595:
590:
588:
587:
586:
585:
568:
566:
565:
556:
551:
550:
534:
532:
531:
526:
524:
523:
522:
521:
504:
502:
501:
492:
487:
486:
423:
421:
420:
415:
409:
407:
396:
354:caesium standard
88:Josephson effect
86:In physics, the
67:
60:
56:
53:
47:
27:
26:
19:
8460:
8459:
8455:
8454:
8453:
8451:
8450:
8449:
8410:
8409:
8408:
8403:
8374:
8344:
8287:
8246:
8233:low temperature
8222:
8201:
8156:
8112:Meissner effect
8065:
8061:Silsbee current
8034:
8000:Ginzburg–Landau
7978:
7973:
7943:
7938:
7882:
7863:Granular matter
7858:Amorphous solid
7844:
7769:
7755:Antiferromagnet
7745:Superparamagnet
7718:Magnetic phases
7709:
7673:
7622:
7583:Bloch's theorem
7556:
7498:
7479:Order parameter
7472:Phase phenomena
7467:
7458:
7390:
7385:
7355:
7354:
7347:
7333:
7329:
7298:
7294:
7285:
7283:
7270:
7269:
7265:
7256:
7254:
7246:
7245:
7241:
7198:
7194:
7155:
7151:
7145:Michael Tinkham
7143:
7139:
7122:
7118:
7103:10.1063/1.89520
7089:(11): 776–778.
7079:
7075:
7040:Physics Letters
7036:
7032:
7025:
7007:
7003:
6994:
6992:
6984:
6983:
6979:
6944:Physica Scripta
6940:
6936:
6897:
6893:
6884:
6880:
6871:
6869:
6868:on 27 July 2011
6865:
6859:rich.phekda.org
6851:
6847:
6816:
6812:
6803:
6801:
6799:The Nobel Prize
6793:
6792:
6788:
6781:
6773:
6769:
6734:
6730:
6723:
6701:
6692:
6657:
6653:
6642:
6638:
6629:
6625:
6550:
6546:
6519:Physics Letters
6515:
6508:
6503:
6498:
6438:Josephson diode
6423:
6393:
6389:
6387:
6384:
6383:
6366:
6362:
6360:
6357:
6356:
6339:
6335:
6333:
6330:
6329:
6312:
6308:
6306:
6303:
6302:
6285:
6281:
6279:
6276:
6275:
6245:
6241:
6237:
6231:
6227:
6225:
6221:
6209:
6205:
6189:
6185:
6181:
6175:
6171:
6169:
6165:
6153:
6149:
6140:
6136:
6125:
6123:
6120:
6119:
6097:
6095:
6092:
6091:
6070:
6066:
6064:
6061:
6060:
6043:
6039:
6037:
6034:
6033:
6006:
6002:
5994:
5988:
5984:
5977:
5971:
5967:
5964:
5955:
5951:
5949:
5946:
5945:
5925:
5921:
5919:
5916:
5915:
5904:
5883:
5880:
5879:
5862:
5858:
5856:
5853:
5852:
5825:
5807:
5803:
5789:
5780:
5778:
5772:
5768:
5759:
5755:
5753:
5750:
5749:
5729:
5725:
5723:
5720:
5719:
5708:
5653:
5649:
5632:
5629:
5628:
5611:
5606:
5596:
5592:
5583:
5579:
5577:
5574:
5573:
5552:
5545:
5541:
5535:
5531:
5530:
5528:
5520:
5503:
5494:
5490:
5488:
5485:
5484:
5451:
5447:
5422:
5415:
5411:
5405:
5401:
5400:
5398:
5378:
5375:
5374:
5323:
5316:
5312:
5306:
5302:
5301:
5299:
5278:
5273:
5267:
5263:
5262:
5258:
5239:
5235:
5227:
5223:
5222:
5215:
5211:
5210:
5187:
5182:
5170:
5154:
5149:
5134:
5131:
5130:
5110:
5106:
5104:
5101:
5100:
5083:
5079:
5077:
5074:
5073:
5056:
5052:
5050:
5047:
5046:
5029:
5025:
5023:
5020:
5019:
4989:
4974:
4971:
4970:
4931:
4927:
4919:
4916:
4915:
4906:
4877:
4873:
4866:
4860:
4856:
4854:
4830:
4826:
4824:
4821:
4820:
4790:
4784:
4780:
4778:
4757:
4753:
4746:
4740:
4736:
4734:
4717:
4714:
4713:
4683:
4675:
4673:
4648:
4640:
4638:
4620:
4616:
4609:
4603:
4599:
4597:
4589:
4586:
4585:
4550:
4546:
4538:
4536:
4518:
4514:
4501:
4493:
4491:
4481:
4473:
4471:
4458:
4450:
4448:
4446:
4443:
4442:
4434:Now, apply the
4418:
4417:
4403:
4399:
4391:
4389:
4382:
4372:
4364:
4362:
4359:
4358:
4340:
4336:
4329:
4319:
4311:
4309:
4305:
4303:
4300:
4299:
4285:
4258:
4254:
4230:
4226:
4220:
4216:
4207:
4203:
4200: and
4198:
4182:
4177:
4165:
4161:
4159:
4156:
4155:
4106:
4102:
4078:
4074:
4068:
4054:
4044:
4040:
4022: and
4020:
3971:
3966:
3949:
3946:
3945:
3892:
3888:
3871:
3868:
3867:
3851:
3848:
3847:
3841:
3816:
3812:
3806:
3802:
3800:
3797:
3796:
3779:
3775:
3773:
3770:
3769:
3745:
3741:
3739:
3736:
3735:
3732:
3710:
3706:
3704:
3701:
3700:
3683:
3679:
3674:
3671:
3670:
3663:
3632:
3630:
3627:
3626:
3604:
3601:
3600:
3593:
3549:
3541:
3539:
3526:
3518:
3516:
3506:
3500:
3496:
3494:
3486:
3483:
3482:
3453:
3448:
3442:
3438:
3430:
3427:
3426:
3387:
3383:
3375:
3373:
3349:
3345:
3323:
3315:
3313:
3311:
3308:
3307:
3278:
3273:
3254:
3249:
3240:
3236:
3234:
3231:
3230:
3194:
3192:
3183:
3179:
3177:
3174:
3173:
3170:is defined as:
3127:
3123:
3121:
3118:
3117:
3092:
3089:
3088:
3063:
3060:
3059:
3018:
3016:
3003:
2995:
2993:
2991:
2988:
2987:
2942:
2938:
2921:
2918:
2917:
2894:
2890:
2881:
2877:
2875:
2872:
2871:
2855:
2852:
2851:
2834:
2823:
2822:
2821:
2819:
2816:
2815:
2795:
2784:
2783:
2782:
2773:
2762:
2761:
2760:
2746:
2745:
2743:
2740:
2739:
2702:
2698:
2692:
2688:
2685:
2660:
2651:
2640:
2639:
2638:
2611:
2607:
2601:
2597:
2595:
2588:
2586:
2574:
2563:
2562:
2561:
2559:
2556:
2555:
2516:
2512:
2506:
2502:
2499:
2474:
2462:
2451:
2450:
2449:
2447:
2444:
2443:
2410:
2406:
2398:
2394:
2392:
2377:
2373:
2365:
2361:
2359:
2345:
2341:
2339:
2317:
2312:
2303:
2292:
2291:
2290:
2282:
2278:
2276:
2268:
2265:
2264:
2238:
2234:
2231:
2230:
2228:
2225:
2224:
2185:
2181:
2175:
2171:
2169:
2162:
2160:
2151:
2140:
2139:
2138:
2136:
2133:
2132:
2108:
2104:
2102:
2098:
2092:
2081:
2080:
2079:
2077:
2061:
2057:
2054:
2053:
2051:
2048:
2047:
2002:
1998:
1996:
1992:
1990:
1972:
1968:
1960:
1956:
1954:
1939:
1935:
1927:
1923:
1921:
1905:
1900:
1884:
1880:
1877:
1876:
1871:
1868:
1867:
1848:
1837:
1836:
1835:
1833:
1830:
1829:
1798:
1794:
1786:
1782:
1780:
1766:
1762:
1760:
1738:
1733:
1724:
1713:
1712:
1711:
1703:
1699:
1697:
1678:
1674:
1671:
1670:
1668:
1665:
1664:
1630:
1626:
1618:
1614:
1612:
1598:
1594:
1592:
1573:
1568:
1559:
1548:
1547:
1546:
1538:
1534:
1532:
1513:
1509:
1506:
1505:
1503:
1500:
1499:
1477:
1473:
1464:
1460:
1452:
1449:
1448:
1443:Josephson phase
1415:
1411:
1407:
1403:
1395:
1391:
1389:
1375:
1371:
1367:
1363:
1355:
1351:
1349:
1330:
1325:
1314:
1310:
1306:
1302:
1293:
1282:
1281:
1280:
1272:
1268:
1266:
1247:
1243:
1240:
1239:
1234:
1231:
1230:
1204:
1200:
1196:
1192:
1183:
1172:
1171:
1170:
1162:
1158:
1156:
1137:
1133:
1130:
1129:
1112:
1108:
1104:
1100:
1094:
1083:
1082:
1081:
1067:
1063:
1061:
1050:
1046:
1042:
1038:
1025:
1021:
1018:
1017:
1003:
999:
995:
991:
983:
979:
977:
964:
959:
957:
954:
953:
935:
932:
931:
908:
907:
899:
895:
891:
887:
879:
875:
873:
870:
869:
861:
857:
853:
849:
841:
837:
835:
828:
827:
820:
819:
808:
802:
801:
796:
783:
782:
772:
771:
763:
759:
755:
751:
743:
739:
737:
734:
733:
725:
721:
717:
713:
705:
701:
699:
692:
691:
681:
676:
668:
665:
664:
632:
629:
628:
612:
609:
608:
581:
577:
573:
569:
561:
557:
555:
546:
542:
540:
537:
536:
517:
513:
509:
505:
497:
493:
491:
482:
478:
476:
473:
472:
458:
400:
395:
392:
389:
388:
367:superconducting
255:
206:Physics Letters
201:Physics Letters
181:experiments by
166:Mond Laboratory
154:
144:is achieved by
96:Brian Josephson
92:superconductors
68:
57:
51:
48:
40:help improve it
37:
28:
24:
17:
12:
11:
5:
8458:
8448:
8447:
8442:
8437:
8432:
8427:
8422:
8405:
8404:
8402:
8401:
8396:
8391:
8386:
8381:
8376:
8372:
8368:
8363:
8358:
8352:
8350:
8346:
8345:
8343:
8342:
8337:
8332:
8327:
8322:
8317:
8312:
8310:electromagnets
8307:
8301:
8299:
8293:
8292:
8289:
8288:
8286:
8285:
8280:
8275:
8270:
8265:
8260:
8254:
8252:
8251:By composition
8248:
8247:
8245:
8244:
8239:
8234:
8230:
8228:
8224:
8223:
8221:
8220:
8218:unconventional
8215:
8209:
8207:
8206:By explanation
8203:
8202:
8200:
8199:
8194:
8193:
8192:
8187:
8182:
8173:
8171:
8164:
8162:Classification
8158:
8157:
8155:
8154:
8149:
8144:
8139:
8134:
8129:
8124:
8119:
8114:
8109:
8104:
8099:
8094:
8089:
8084:
8079:
8073:
8071:
8067:
8066:
8064:
8063:
8058:
8053:
8051:critical field
8048:
8042:
8040:
8036:
8035:
8033:
8032:
8027:
8022:
8020:Mattis–Bardeen
8017:
8012:
8007:
8005:Kohn–Luttinger
8002:
7997:
7992:
7986:
7984:
7980:
7979:
7972:
7971:
7964:
7957:
7949:
7940:
7939:
7937:
7936:
7924:
7921:Physics Portal
7912:
7900:
7887:
7884:
7883:
7881:
7880:
7875:
7870:
7868:Liquid crystal
7865:
7860:
7854:
7852:
7846:
7845:
7843:
7842:
7837:
7836:
7835:
7830:
7820:
7815:
7810:
7805:
7800:
7795:
7790:
7785:
7779:
7777:
7775:Quasiparticles
7771:
7770:
7768:
7767:
7762:
7757:
7752:
7747:
7742:
7737:
7735:Superdiamagnet
7732:
7727:
7721:
7719:
7715:
7714:
7711:
7710:
7708:
7707:
7702:
7697:
7692:
7687:
7681:
7679:
7675:
7674:
7672:
7671:
7666:
7661:
7659:Superconductor
7656:
7651:
7646:
7641:
7639:Mott insulator
7636:
7630:
7628:
7624:
7623:
7621:
7620:
7615:
7610:
7605:
7600:
7595:
7590:
7585:
7580:
7575:
7570:
7564:
7562:
7558:
7557:
7555:
7554:
7549:
7544:
7539:
7534:
7529:
7524:
7519:
7513:
7511:
7504:
7500:
7499:
7497:
7496:
7491:
7486:
7481:
7475:
7473:
7469:
7468:
7461:
7459:
7457:
7456:
7451:
7446:
7441:
7436:
7431:
7426:
7421:
7416:
7411:
7406:
7400:
7398:
7392:
7391:
7384:
7383:
7376:
7369:
7361:
7353:
7352:
7345:
7327:
7292:
7263:
7239:
7192:
7149:
7137:
7116:
7073:
7046:(6): 563–565.
7030:
7023:
7001:
6977:
6934:
6891:
6878:
6845:
6810:
6786:
6767:
6728:
6721:
6690:
6671:(8): 316–318.
6651:
6636:
6623:
6621:
6620:
6564:(2): 251–254.
6544:
6525:(7): 251–253.
6505:
6504:
6502:
6499:
6497:
6496:
6491:
6486:
6481:
6475:
6470:
6465:
6460:
6455:
6450:
6445:
6440:
6435:
6430:
6424:
6422:
6419:
6396:
6392:
6369:
6365:
6342:
6338:
6315:
6311:
6288:
6284:
6272:
6271:
6260:
6256:
6248:
6244:
6240:
6234:
6230:
6224:
6220:
6217:
6212:
6208:
6204:
6200:
6192:
6188:
6184:
6178:
6174:
6168:
6164:
6161:
6156:
6152:
6148:
6143:
6139:
6135:
6131:
6128:
6103:
6100:
6073:
6069:
6046:
6042:
6030:
6029:
6018:
6009:
6005:
6000:
5997:
5991:
5987:
5983:
5980:
5974:
5970:
5963:
5958:
5954:
5928:
5924:
5908:magnetic field
5903:
5900:
5887:
5865:
5861:
5849:
5848:
5837:
5832:
5829:
5824:
5821:
5818:
5815:
5810:
5806:
5802:
5796:
5792:
5787:
5783:
5775:
5771:
5767:
5758:
5728:
5707:
5706:The RCSJ model
5704:
5679:
5676:
5673:
5670:
5667:
5664:
5661:
5656:
5652:
5648:
5645:
5642:
5639:
5636:
5614:
5609:
5605:
5599:
5595:
5591:
5586:
5582:
5558:
5555:
5548:
5544:
5538:
5534:
5527:
5523:
5519:
5516:
5513:
5510:
5506:
5502:
5497:
5493:
5481:
5480:
5469:
5465:
5462:
5459:
5454:
5450:
5446:
5443:
5440:
5437:
5434:
5428:
5425:
5418:
5414:
5408:
5404:
5397:
5394:
5391:
5388:
5385:
5382:
5368:state function
5360:
5359:
5348:
5344:
5341:
5338:
5335:
5329:
5326:
5319:
5315:
5309:
5305:
5298:
5295:
5291:
5284:
5281:
5277:
5270:
5266:
5261:
5256:
5253:
5250:
5247:
5242:
5238:
5230:
5226:
5218:
5214:
5209:
5205:
5202:
5198:
5195:
5190:
5185:
5181:
5177:
5173:
5168:
5165:
5162:
5157:
5152:
5148:
5144:
5141:
5138:
5113:
5109:
5086:
5082:
5059:
5055:
5032:
5028:
5016:
5015:
5004:
5000:
4996:
4992:
4988:
4984:
4981:
4978:
4960:
4959:
4948:
4945:
4942:
4939:
4934:
4930:
4926:
4923:
4905:
4902:
4880:
4876:
4872:
4869:
4863:
4859:
4853:
4850:
4847:
4844:
4841:
4838:
4833:
4829:
4817:
4816:
4805:
4799:
4796:
4793:
4787:
4783:
4777:
4771:
4768:
4765:
4760:
4756:
4752:
4749:
4743:
4739:
4733:
4730:
4727:
4724:
4721:
4707:
4706:
4695:
4689:
4686:
4681:
4678:
4672:
4669:
4666:
4663:
4660:
4654:
4651:
4646:
4643:
4634:
4631:
4628:
4623:
4619:
4615:
4612:
4606:
4602:
4596:
4593:
4575:
4574:
4563:
4560:
4553:
4549:
4544:
4541:
4535:
4532:
4529:
4526:
4521:
4517:
4513:
4507:
4504:
4499:
4496:
4487:
4484:
4479:
4476:
4470:
4464:
4461:
4456:
4453:
4432:
4431:
4416:
4413:
4406:
4402:
4397:
4394:
4388:
4385:
4383:
4378:
4375:
4370:
4367:
4361:
4360:
4357:
4354:
4351:
4348:
4343:
4339:
4335:
4332:
4330:
4325:
4322:
4317:
4314:
4308:
4307:
4284:
4281:
4266:
4261:
4257:
4253:
4250:
4247:
4244:
4241:
4236:
4233:
4229:
4223:
4219:
4215:
4206:
4197:
4194:
4188:
4185:
4181:
4176:
4173:
4164:
4141:
4138:
4135:
4132:
4129:
4126:
4123:
4120:
4117:
4114:
4109:
4105:
4101:
4098:
4095:
4092:
4089:
4086:
4081:
4077:
4071:
4066:
4063:
4060:
4057:
4053:
4047:
4043:
4039:
4036:
4033:
4030:
4027:
4019:
4016:
4013:
4010:
4007:
4004:
4001:
3998:
3995:
3992:
3989:
3986:
3983:
3977:
3974:
3970:
3965:
3962:
3959:
3956:
3953:
3933:
3930:
3927:
3924:
3921:
3918:
3915:
3912:
3909:
3906:
3903:
3900:
3895:
3891:
3887:
3884:
3881:
3878:
3875:
3855:
3840:
3837:
3822:
3819:
3815:
3809:
3805:
3795:and frequency
3782:
3778:
3751:
3748:
3744:
3731:
3728:
3713:
3709:
3686:
3682:
3678:
3662:
3659:
3641:
3638:
3635:
3614:
3611:
3608:
3592:
3589:
3562:
3555:
3552:
3547:
3544:
3538:
3532:
3529:
3524:
3521:
3512:
3509:
3503:
3499:
3493:
3490:
3466:
3459:
3456:
3452:
3445:
3441:
3437:
3434:
3423:If we define:
3410:
3406:
3403:
3400:
3397:
3390:
3386:
3381:
3378:
3372:
3369:
3366:
3363:
3360:
3357:
3352:
3348:
3344:
3341:
3338:
3335:
3329:
3326:
3321:
3318:
3291:
3284:
3281:
3277:
3272:
3269:
3266:
3260:
3257:
3253:
3248:
3243:
3239:
3210:
3204:
3200:
3197:
3191:
3186:
3182:
3130:
3126:
3105:
3102:
3099:
3096:
3076:
3073:
3070:
3067:
3040:
3036:
3033:
3030:
3027:
3024:
3021:
3015:
3009:
3006:
3001:
2998:
2971:
2968:
2965:
2962:
2959:
2956:
2953:
2950:
2945:
2941:
2937:
2934:
2931:
2928:
2925:
2897:
2893:
2889:
2884:
2880:
2859:
2837:
2830:
2827:
2798:
2791:
2788:
2781:
2776:
2769:
2766:
2759:
2753:
2750:
2725:
2722:
2719:
2716:
2713:
2705:
2701:
2695:
2691:
2684:
2681:
2678:
2675:
2672:
2667:
2664:
2659:
2654:
2647:
2644:
2636:
2633:
2630:
2627:
2622:
2614:
2610:
2604:
2600:
2594:
2591:
2585:
2582:
2577:
2570:
2567:
2539:
2536:
2533:
2530:
2527:
2519:
2515:
2509:
2505:
2498:
2495:
2492:
2489:
2486:
2481:
2478:
2473:
2470:
2465:
2458:
2455:
2427:
2424:
2419:
2416:
2413:
2409:
2401:
2397:
2391:
2388:
2383:
2380:
2376:
2368:
2364:
2358:
2355:
2348:
2344:
2338:
2335:
2332:
2329:
2323:
2320:
2316:
2311:
2306:
2299:
2296:
2285:
2281:
2275:
2272:
2247:
2241:
2237:
2210:
2207:
2204:
2201:
2196:
2188:
2184:
2178:
2174:
2168:
2165:
2159:
2154:
2147:
2144:
2111:
2107:
2101:
2095:
2088:
2085:
2076:
2070:
2064:
2060:
2033:
2030:
2027:
2024:
2021:
2018:
2013:
2005:
2001:
1995:
1989:
1986:
1981:
1978:
1975:
1971:
1963:
1959:
1953:
1950:
1945:
1942:
1938:
1930:
1926:
1920:
1917:
1911:
1908:
1904:
1899:
1893:
1887:
1883:
1875:
1851:
1844:
1841:
1815:
1812:
1807:
1804:
1801:
1797:
1789:
1785:
1779:
1776:
1769:
1765:
1759:
1756:
1753:
1747:
1744:
1741:
1737:
1732:
1727:
1720:
1717:
1706:
1702:
1696:
1693:
1687:
1681:
1677:
1644:
1641:
1636:
1633:
1629:
1621:
1617:
1611:
1608:
1601:
1597:
1591:
1588:
1585:
1579:
1576:
1572:
1567:
1562:
1555:
1552:
1541:
1537:
1531:
1528:
1522:
1516:
1512:
1485:
1480:
1476:
1472:
1467:
1463:
1459:
1456:
1428:
1425:
1418:
1414:
1410:
1406:
1398:
1394:
1388:
1385:
1378:
1374:
1370:
1366:
1358:
1354:
1348:
1345:
1342:
1336:
1333:
1329:
1324:
1317:
1313:
1309:
1305:
1301:
1296:
1289:
1286:
1275:
1271:
1265:
1262:
1256:
1250:
1246:
1238:
1214:
1207:
1203:
1199:
1195:
1191:
1186:
1179:
1176:
1165:
1161:
1155:
1152:
1146:
1140:
1136:
1128:
1125:
1122:
1115:
1111:
1107:
1103:
1097:
1090:
1087:
1080:
1077:
1070:
1066:
1060:
1053:
1049:
1045:
1041:
1034:
1028:
1024:
1016:
1013:
1006:
1002:
998:
994:
986:
982:
976:
970:
967:
963:
939:
917:
912:
902:
898:
894:
890:
882:
878:
872:
871:
864:
860:
856:
852:
844:
840:
834:
833:
831:
824:
818:
815:
812:
809:
807:
804:
803:
800:
797:
795:
792:
789:
788:
786:
781:
776:
766:
762:
758:
754:
746:
742:
736:
735:
728:
724:
720:
716:
708:
704:
698:
697:
695:
687:
684:
680:
675:
672:
661:is therefore:
642:
639:
636:
616:
601:wave functions
584:
580:
576:
572:
564:
560:
554:
549:
545:
520:
516:
512:
508:
500:
496:
490:
485:
481:
457:
454:
453:
452:
443:
425:
412:
406:
403:
399:
379:
370:
360:
330:
319:
309:
306:proxy variable
298:
254:
251:
153:
150:
70:
69:
52:September 2018
31:
29:
22:
15:
9:
6:
4:
3:
2:
8457:
8446:
8443:
8441:
8438:
8436:
8433:
8431:
8428:
8426:
8423:
8421:
8418:
8417:
8415:
8400:
8397:
8395:
8392:
8390:
8387:
8385:
8382:
8380:
8377:
8375:
8369:
8367:
8364:
8362:
8359:
8357:
8354:
8353:
8351:
8347:
8341:
8338:
8336:
8333:
8331:
8328:
8326:
8323:
8321:
8318:
8316:
8313:
8311:
8308:
8306:
8303:
8302:
8300:
8298:
8294:
8284:
8281:
8279:
8276:
8274:
8271:
8269:
8268:heavy fermion
8266:
8264:
8261:
8259:
8256:
8255:
8253:
8249:
8243:
8240:
8238:
8235:
8232:
8231:
8229:
8225:
8219:
8216:
8214:
8211:
8210:
8208:
8204:
8198:
8197:ferromagnetic
8195:
8191:
8188:
8186:
8183:
8181:
8178:
8177:
8175:
8174:
8172:
8168:
8165:
8163:
8159:
8153:
8150:
8148:
8145:
8143:
8142:supercurrents
8140:
8138:
8135:
8133:
8130:
8128:
8125:
8123:
8120:
8118:
8115:
8113:
8110:
8108:
8105:
8103:
8100:
8098:
8095:
8093:
8090:
8088:
8085:
8083:
8080:
8078:
8075:
8074:
8072:
8068:
8062:
8059:
8057:
8054:
8052:
8049:
8047:
8044:
8043:
8041:
8037:
8031:
8028:
8026:
8023:
8021:
8018:
8016:
8013:
8011:
8008:
8006:
8003:
8001:
7998:
7996:
7993:
7991:
7988:
7987:
7985:
7981:
7977:
7970:
7965:
7963:
7958:
7956:
7951:
7950:
7947:
7935:
7934:
7925:
7923:
7922:
7917:
7913:
7911:
7910:
7901:
7899:
7898:
7889:
7888:
7885:
7879:
7876:
7874:
7871:
7869:
7866:
7864:
7861:
7859:
7856:
7855:
7853:
7851:
7847:
7841:
7838:
7834:
7831:
7829:
7826:
7825:
7824:
7821:
7819:
7816:
7814:
7811:
7809:
7806:
7804:
7801:
7799:
7796:
7794:
7791:
7789:
7786:
7784:
7781:
7780:
7778:
7776:
7772:
7766:
7763:
7761:
7758:
7756:
7753:
7751:
7748:
7746:
7743:
7741:
7738:
7736:
7733:
7731:
7728:
7726:
7723:
7722:
7720:
7716:
7706:
7703:
7701:
7698:
7696:
7693:
7691:
7688:
7686:
7683:
7682:
7680:
7676:
7670:
7667:
7665:
7662:
7660:
7657:
7655:
7652:
7650:
7647:
7645:
7644:Semiconductor
7642:
7640:
7637:
7635:
7632:
7631:
7629:
7625:
7619:
7616:
7614:
7613:Hubbard model
7611:
7609:
7606:
7604:
7601:
7599:
7596:
7594:
7591:
7589:
7586:
7584:
7581:
7579:
7576:
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7569:
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7553:
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7528:
7525:
7523:
7520:
7518:
7515:
7514:
7512:
7508:
7505:
7501:
7495:
7492:
7490:
7487:
7485:
7482:
7480:
7477:
7476:
7474:
7470:
7465:
7455:
7452:
7450:
7447:
7445:
7442:
7440:
7437:
7435:
7432:
7430:
7427:
7425:
7422:
7420:
7417:
7415:
7412:
7410:
7407:
7405:
7402:
7401:
7399:
7397:
7393:
7389:
7382:
7377:
7375:
7370:
7368:
7363:
7362:
7359:
7348:
7342:
7338:
7331:
7323:
7319:
7315:
7311:
7307:
7303:
7296:
7282:on 2021-06-13
7281:
7277:
7273:
7267:
7253:
7249:
7243:
7235:
7231:
7227:
7223:
7219:
7215:
7211:
7207:
7203:
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7188:
7184:
7180:
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7164:
7160:
7153:
7146:
7141:
7132:
7127:
7120:
7112:
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7104:
7100:
7096:
7092:
7088:
7084:
7077:
7069:
7065:
7061:
7057:
7053:
7049:
7045:
7041:
7034:
7026:
7020:
7016:
7012:
7005:
6991:
6987:
6981:
6973:
6969:
6965:
6961:
6957:
6953:
6949:
6945:
6938:
6930:
6926:
6922:
6918:
6914:
6910:
6906:
6902:
6895:
6888:
6882:
6864:
6860:
6856:
6849:
6841:
6837:
6833:
6829:
6825:
6821:
6814:
6800:
6796:
6790:
6777:
6771:
6763:
6759:
6755:
6751:
6747:
6743:
6739:
6732:
6724:
6722:9780309084086
6718:
6714:
6709:
6708:
6699:
6697:
6695:
6686:
6682:
6678:
6674:
6670:
6666:
6662:
6655:
6647:
6640:
6633:
6627:
6617:
6613:
6609:
6605:
6601:
6597:
6591:
6590:
6587:
6583:
6579:
6575:
6571:
6567:
6563:
6559:
6555:
6548:
6540:
6536:
6532:
6528:
6524:
6520:
6513:
6511:
6506:
6495:
6492:
6490:
6487:
6485:
6482:
6479:
6476:
6474:
6471:
6469:
6466:
6464:
6461:
6459:
6456:
6454:
6451:
6449:
6446:
6444:
6441:
6439:
6436:
6434:
6431:
6429:
6426:
6425:
6418:
6416:
6412:
6394:
6390:
6367:
6363:
6340:
6336:
6313:
6309:
6286:
6282:
6258:
6254:
6246:
6242:
6238:
6232:
6228:
6222:
6218:
6215:
6210:
6206:
6202:
6198:
6190:
6186:
6182:
6176:
6172:
6166:
6162:
6159:
6154:
6150:
6146:
6141:
6137:
6133:
6129:
6126:
6118:
6117:
6116:
6101:
6098:
6089:
6071:
6067:
6044:
6016:
6007:
6003:
5998:
5995:
5989:
5985:
5981:
5978:
5972:
5961:
5956:
5952:
5944:
5943:
5942:
5926:
5922:
5913:
5909:
5899:
5885:
5863:
5859:
5835:
5830:
5827:
5822:
5819:
5816:
5813:
5808:
5804:
5800:
5794:
5785:
5773:
5769:
5765:
5756:
5748:
5747:
5746:
5726:
5717:
5712:
5703:
5700:
5696:
5691:
5674:
5671:
5668:
5665:
5662:
5654:
5650:
5646:
5640:
5634:
5612:
5607:
5603:
5597:
5593:
5589:
5584:
5580:
5556:
5553:
5546:
5542:
5536:
5525:
5514:
5508:
5500:
5495:
5491:
5467:
5463:
5460:
5457:
5452:
5448:
5444:
5441:
5438:
5435:
5432:
5426:
5423:
5416:
5412:
5406:
5395:
5392:
5386:
5380:
5373:
5372:
5371:
5369:
5365:
5346:
5342:
5339:
5336:
5327:
5324:
5317:
5313:
5307:
5296:
5293:
5289:
5282:
5279:
5275:
5268:
5259:
5251:
5248:
5245:
5240:
5236:
5228:
5224:
5216:
5212:
5207:
5203:
5193:
5188:
5183:
5179:
5175:
5171:
5163:
5160:
5155:
5150:
5146:
5142:
5139:
5129:
5128:
5127:
5111:
5107:
5084:
5080:
5057:
5053:
5030:
5026:
5002:
4998:
4990:
4979:
4976:
4969:
4968:
4967:
4965:
4964:Faraday's law
4946:
4943:
4940:
4937:
4932:
4928:
4924:
4921:
4914:
4913:
4912:
4909:
4901:
4897:
4878:
4874:
4870:
4867:
4861:
4851:
4845:
4839:
4836:
4831:
4827:
4803:
4797:
4794:
4791:
4785:
4781:
4775:
4769:
4766:
4763:
4758:
4754:
4750:
4747:
4741:
4731:
4725:
4719:
4712:
4711:
4710:
4693:
4687:
4679:
4667:
4661:
4658:
4652:
4644:
4632:
4629:
4626:
4621:
4617:
4613:
4610:
4604:
4594:
4591:
4584:
4583:
4582:
4580:
4561:
4558:
4551:
4542:
4539:
4533:
4530:
4527:
4524:
4519:
4515:
4511:
4505:
4497:
4485:
4477:
4468:
4462:
4454:
4441:
4440:
4439:
4437:
4414:
4411:
4404:
4395:
4392:
4386:
4384:
4376:
4368:
4355:
4352:
4349:
4346:
4341:
4337:
4333:
4331:
4323:
4315:
4298:
4297:
4296:
4293:
4291:
4280:
4277:
4264:
4259:
4255:
4251:
4248:
4242:
4234:
4231:
4227:
4221:
4217:
4213:
4204:
4195:
4192:
4186:
4183:
4179:
4174:
4171:
4162:
4152:
4139:
4133:
4130:
4124:
4121:
4118:
4112:
4107:
4103:
4096:
4093:
4087:
4079:
4075:
4061:
4058:
4055:
4051:
4045:
4041:
4037:
4031:
4025:
4017:
4008:
4005:
3999:
3996:
3993:
3990:
3987:
3981:
3975:
3972:
3968:
3963:
3957:
3951:
3928:
3925:
3919:
3916:
3913:
3910:
3907:
3904:
3901:
3898:
3893:
3889:
3885:
3879:
3873:
3853:
3846:
3836:
3820:
3817:
3813:
3807:
3803:
3780:
3776:
3767:
3749:
3746:
3742:
3727:
3711:
3707:
3684:
3680:
3676:
3668:
3658:
3639:
3636:
3633:
3612:
3609:
3606:
3597:
3588:
3586:
3582:
3578:
3573:
3560:
3553:
3550:
3542:
3536:
3530:
3522:
3510:
3507:
3501:
3491:
3488:
3480:
3477:
3464:
3457:
3454:
3450:
3443:
3435:
3424:
3421:
3408:
3401:
3395:
3388:
3379:
3376:
3370:
3361:
3355:
3350:
3346:
3339:
3336:
3333:
3327:
3319:
3305:
3302:
3289:
3282:
3279:
3275:
3270:
3267:
3264:
3258:
3255:
3251:
3246:
3241:
3228:
3226:
3221:
3208:
3202:
3198:
3195:
3189:
3184:
3180:
3171:
3169:
3164:
3162:
3158:
3154:
3150:
3146:
3128:
3124:
3100:
3094:
3071:
3065:
3056:
3055:
3031:
3025:
3022:
3019:
3013:
3007:
2999:
2985:
2984:
2963:
2957:
2951:
2948:
2943:
2939:
2935:
2929:
2923:
2915:
2913:
2895:
2891:
2887:
2882:
2878:
2857:
2835:
2828:
2825:
2814:
2796:
2789:
2786:
2779:
2774:
2767:
2764:
2757:
2751:
2748:
2736:
2723:
2717:
2714:
2711:
2703:
2699:
2693:
2689:
2682:
2679:
2676:
2673:
2662:
2657:
2652:
2645:
2642:
2634:
2631:
2628:
2625:
2612:
2608:
2602:
2598:
2592:
2589:
2583:
2580:
2575:
2568:
2565:
2553:
2550:
2537:
2531:
2528:
2525:
2517:
2513:
2507:
2503:
2496:
2493:
2490:
2487:
2476:
2471:
2468:
2463:
2456:
2453:
2441:
2440:which gives:
2438:
2425:
2417:
2414:
2411:
2407:
2399:
2395:
2389:
2386:
2381:
2378:
2374:
2366:
2362:
2356:
2353:
2346:
2342:
2336:
2333:
2330:
2318:
2314:
2309:
2304:
2297:
2294:
2283:
2279:
2273:
2270:
2262:
2245:
2239:
2235:
2221:
2208:
2205:
2202:
2199:
2186:
2182:
2176:
2172:
2166:
2163:
2157:
2152:
2145:
2142:
2130:
2109:
2105:
2099:
2093:
2086:
2083:
2074:
2068:
2062:
2058:
2044:
2031:
2028:
2025:
2022:
2019:
2016:
2003:
1999:
1993:
1987:
1979:
1976:
1973:
1969:
1961:
1957:
1951:
1948:
1943:
1940:
1936:
1928:
1924:
1918:
1906:
1902:
1897:
1891:
1885:
1881:
1873:
1865:
1849:
1842:
1839:
1826:
1813:
1805:
1802:
1799:
1795:
1787:
1783:
1777:
1774:
1767:
1763:
1757:
1754:
1742:
1739:
1735:
1730:
1725:
1718:
1715:
1704:
1700:
1694:
1691:
1685:
1679:
1675:
1662:
1661:equation is:
1660:
1655:
1642:
1634:
1631:
1627:
1619:
1615:
1609:
1606:
1599:
1595:
1589:
1586:
1574:
1570:
1565:
1560:
1553:
1550:
1539:
1535:
1529:
1526:
1520:
1514:
1510:
1497:
1483:
1478:
1474:
1470:
1465:
1461:
1457:
1454:
1446:
1444:
1439:
1426:
1416:
1412:
1408:
1404:
1396:
1392:
1386:
1383:
1376:
1372:
1368:
1364:
1356:
1352:
1346:
1343:
1331:
1327:
1322:
1315:
1311:
1307:
1303:
1294:
1287:
1284:
1273:
1269:
1263:
1260:
1254:
1248:
1244:
1228:
1225:
1212:
1205:
1201:
1197:
1193:
1184:
1177:
1174:
1163:
1159:
1153:
1150:
1144:
1138:
1134:
1123:
1113:
1109:
1105:
1101:
1095:
1088:
1085:
1078:
1068:
1064:
1058:
1051:
1047:
1043:
1039:
1032:
1026:
1022:
1014:
1004:
1000:
996:
992:
984:
980:
968:
951:
937:
928:
915:
910:
900:
896:
892:
888:
880:
876:
862:
858:
854:
850:
842:
838:
829:
822:
816:
813:
810:
805:
798:
793:
790:
784:
779:
774:
764:
760:
756:
752:
744:
740:
726:
722:
718:
714:
706:
702:
693:
685:
670:
662:
660:
656:
640:
637:
634:
614:
606:
602:
582:
578:
574:
570:
562:
558:
552:
547:
543:
518:
514:
510:
506:
498:
494:
488:
483:
479:
471:
462:
451:
447:
444:
441:
437:
434:such as in a
433:
429:
426:
410:
404:
401:
397:
387:
383:
380:
378:
374:
371:
368:
364:
361:
359:
355:
351:
347:
343:
339:
335:
332:In precision
331:
328:
324:
320:
317:
316:magnetometers
313:
310:
307:
303:
299:
296:
292:
288:
287:
286:
284:
280:
276:
272:
264:
259:
250:
248:
244:
240:
235:
232:
228:
223:
221:
217:
213:
212:
207:
203:
202:
195:
190:
187:
184:
179:
175:
171:
167:
163:
162:Brian Pippard
158:
149:
147:
143:
139:
135:
131:
127:
123:
118:
116:
112:
108:
103:
101:
97:
93:
89:
81:
76:
66:
63:
55:
45:
41:
35:
32:This article
30:
21:
20:
8278:oxypnictides
8213:conventional
8152:superstripes
8101:
8097:flux pumping
8092:flux pinning
8087:Cooper pairs
7931:
7919:
7907:
7895:
7813:Pines' demon
7552:Kondo effect
7546:
7454:Time crystal
7337:Supraleitung
7336:
7330:
7305:
7301:
7295:
7284:. Retrieved
7280:the original
7275:
7266:
7255:. Retrieved
7251:
7242:
7209:
7205:
7195:
7162:
7158:
7152:
7140:
7119:
7086:
7082:
7076:
7043:
7039:
7033:
7013:. New York:
7010:
7004:
6993:. Retrieved
6989:
6980:
6947:
6943:
6937:
6904:
6900:
6894:
6886:
6881:
6870:. Retrieved
6863:the original
6858:
6848:
6823:
6819:
6813:
6802:. Retrieved
6798:
6789:
6770:
6745:
6741:
6731:
6706:
6668:
6664:
6654:
6639:
6631:
6626:
6599:
6595:
6561:
6557:
6547:
6522:
6518:
6273:
6031:
5905:
5850:
5713:
5709:
5697:accumulates
5692:
5482:
5361:
5017:
4961:
4910:
4907:
4898:
4818:
4708:
4576:
4433:
4294:
4286:
4278:
4153:
3842:
3733:
3664:
3656:
3574:
3481:
3478:
3425:
3422:
3306:
3303:
3229:
3222:
3172:
3165:
3160:
3156:
3152:
3148:
3144:
3057:
3053:
2982:
2911:
2737:
2554:
2551:
2442:
2439:
2263:
2222:
2131:
2045:
1866:
1827:
1663:
1656:
1498:
1447:
1442:
1440:
1229:
1226:
952:
929:
663:
605:Cooper pairs
467:
338:reproducible
268:
253:Applications
243:Cooper pairs
236:
230:
224:
216:John Bardeen
209:
205:
199:
197:
192:
188:
183:Ivar Giaever
159:
155:
119:
110:
107:supercurrent
104:
87:
85:
58:
49:
33:
8137:SU(2) color
8117:Homes's law
7850:Soft matter
7750:Ferromagnet
7568:Drude model
7537:Berry phase
7517:Hall effect
6090:(A/m), and
2129:, we have:
295:micrometres
8414:Categories
8273:iron-based
8132:reentrance
7765:Spin glass
7760:Metamagnet
7740:Paramagnet
7627:Conduction
7603:BCS theory
7444:Superfluid
7439:Supersolid
7346:3527403485
7308:(2): 169.
7286:2020-01-11
7257:2020-01-03
6995:2020-01-03
6872:2011-04-21
6826:(6): 195.
6804:2023-03-01
6776:US3335363A
6748:(6): 230.
6602:(3): 1–5.
6501:References
6484:Semifluxon
6409:are their
4436:chain rule
436:flux qubit
352:takes the
327:superfluid
325:) are the
273:(of which
124:, such as
8070:Phenomena
7823:Polariton
7730:Diamagnet
7678:Couplings
7654:Conductor
7649:Semimetal
7634:Insulator
7510:Phenomena
7434:Fermi gas
7187:0021-8979
7111:0003-6951
7068:0031-9163
6972:250887469
6866:(website)
6391:λ
6364:λ
6243:λ
6219:
6207:λ
6187:λ
6163:
6151:λ
6041:Φ
5986:μ
5982:π
5969:Φ
5953:λ
5923:λ
5820:φ
5817:
5745:becomes:
5675:φ
5672:
5666:−
5641:φ
5557:π
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5464:φ
5461:
5445:−
5439:φ
5436:
5427:π
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5252:φ
5249:
5225:φ
5213:φ
5208:∫
5201:Φ
5180:∫
5147:∫
5137:Δ
5108:φ
5054:φ
4987:Φ
4944:φ
4941:
4871:π
4858:Φ
4798:φ
4795:
4770:φ
4767:
4751:π
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4726:φ
4685:∂
4677:∂
4668:φ
4650:∂
4642:∂
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4630:
4614:π
4601:Φ
4548:Φ
4543:π
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4503:∂
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4475:∂
4460:∂
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4401:Φ
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4350:
4324:φ
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4313:∂
4256:φ
4252:
4232:−
4193:ω
4180:ℏ
4131:ω
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4097:
4070:∞
4065:∞
4062:−
4052:∑
4006:ω
4000:
3982:ω
3969:ℏ
3926:ω
3920:
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3890:φ
3874:φ
3854:ω
3677:−
3667:tunneling
3546:Φ
3528:∂
3523:φ
3520:∂
3511:π
3498:Φ
3458:π
3451:φ
3440:Φ
3433:Φ
3385:Φ
3380:π
3340:π
3325:∂
3320:φ
3317:∂
3276:ℏ
3271:π
3238:Φ
3039:ℏ
3005:∂
3000:φ
2997:∂
2958:φ
2952:
2888:≈
2829:˙
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2621:ℏ
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2569:˙
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2480:ℏ
2472:−
2457:˙
2454:ϕ
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2322:ℏ
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2246:˙
2206:φ
2203:
2195:ℏ
2146:˙
2087:˙
2069:˙
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2026:
2017:⋅
2012:ℏ
1980:φ
1974:−
1949:−
1944:φ
1910:ℏ
1892:˙
1843:˙
1840:ϕ
1806:φ
1800:−
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1471:−
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1110:ϕ
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1086:ϕ
1048:ϕ
1033:˙
1001:ϕ
966:∂
962:∂
897:ϕ
859:ϕ
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761:ϕ
723:ϕ
683:∂
679:∂
674:ℏ
657:for this
579:ϕ
544:ψ
515:ϕ
480:ψ
342:frequency
334:metrology
291:thin-film
227:Bell Labs
178:Bell Labs
8305:cryotron
8263:cuprates
8258:covalent
8015:Matthias
7983:Theories
7897:Category
7878:Colloids
6929:10040529
6592:Also in
6586:54748764
6421:See also
6130:′
6102:′
5999:′
1657:and its
323:SHeQUIDs
297:or less.
8435:Sensors
8399:more...
8283:organic
7909:Commons
7873:Polymer
7840:Polaron
7818:Plasmon
7798:Exciton
7310:Bibcode
7234:9944915
7214:Bibcode
7167:Bibcode
7091:Bibcode
7048:Bibcode
6952:Bibcode
6950:: 165.
6909:Bibcode
6828:Bibcode
6750:Bibcode
6673:Bibcode
6604:Bibcode
6566:Bibcode
6527:Bibcode
6086:is the
5714:As per
2870:, when
346:voltage
168:of the
164:at the
152:History
38:Please
8176:Types
8010:London
7808:Phonon
7803:Magnon
7561:Theory
7419:Plasma
7409:Liquid
7343:
7232:
7185:
7109:
7066:
7021:
6970:
6927:
6782:
6719:
6584:
6480:(RSFQ)
6274:where
6032:where
4819:Here,
3058:where
2046:Since
432:qubits
348:. The
312:SQUIDs
281:, and
132:, and
126:SQUIDs
8389:TBCCO
8361:BSCCO
8340:wires
8335:SQUID
7783:Anyon
7404:Solid
7126:arXiv
6968:S2CID
6582:S2CID
5483:Here
304:is a
8394:YBCO
8384:NbTi
8379:NbSn
8366:LBCO
7793:Hole
7341:ISBN
7230:PMID
7183:ISSN
7107:ISSN
7064:ISSN
7019:ISBN
6925:PMID
6717:ISBN
6382:and
6328:and
6216:tanh
6160:tanh
5364:path
3699:and
3166:The
3087:and
382:RSFQ
358:volt
344:and
300:The
261:The
176:, a
142:volt
138:NIST
134:RSFQ
8371:MgB
8320:NMR
8315:MRI
8190:1.5
8030:WHH
8025:RVB
7990:BCS
7414:Gas
7318:doi
7222:doi
7175:doi
7099:doi
7056:doi
6960:doi
6948:T76
6917:doi
6836:doi
6758:doi
6713:117
6681:doi
6612:doi
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6535:doi
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5761:ext
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5458:cos
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4627:cos
4525:cos
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4249:sin
4094:sin
3997:cos
3917:sin
3159:or
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2983:(1)
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603:of
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