Current - phase relation of the SNS junction in a supercon - ducting loop

– We study the current-phase relation of the superconductor/normal/superconductor (SNS) junction imbedded in a superconducting loop. Considering the current conservation and free energy minimum conditions, we obtain the persistent currents of the SNS loop. At finite temperature we can explain the experimentally observed highly non-sinusoidal currents which have maxima near the zero external flux. Introduction. – Physically interesting superconducting loops with junctions are the superconducting quantum interference device (SQUID) and the superconductor/normal/superconductor loop with long normal sector (SNlongS loop). Both are mesoscopic size and yield persistent currents when a magnetic flux threads the loop. The thickness of the Josephson junctions in SQUID loop is much smaller than the superconducting coherence length, but the thickness of normal segment d of SNlongS loop can be larger than that. The persistent current in the former system flows by tunneling the Josephson junction, while that in the latter by the long range proximity effect. Since these two loops are very different in nature, we can anticipate a different current-phase relation for SNlongS loop, but it was not explicitly demonstrated in previous studies for the superconductor/normal/superconductor hybrid junction [1–3] and for the SNlongS loop [4, 5] in connection with the Andreev reflection process [6]. The current described by the motion of a pair of electron and hole in the normal sector changes into that by a Cooper pair in the superconducting sector. There is an intermediate region near the edge of superconductor, where the current is described by quasiparticles and quasiholes.Then the current carried by the electrons and the holes in the normal sector should be the same as that carried by quasiparticles and quasiholes in the intermediate region. This current conservation condition can be satisfied by considering that two wave vectors of the quasiparticle and the quasihole can be different from each other like those of electron and hole in the normal sector. In solving the Bogoliubov-de Gennes (BdG) equation, we consider the average energy of a pair of particles is a dynamic variable rather than a constant chemical (∗) E-mail: [email protected]