Some novel effects in superconducting nanojunctions

Abstract

In this paper we address several new developments in the theory of dc Josephson effect in superconducting weak links. We analyze an interplay between quantum interference effects and Andreev reflection in SNS nanojunctions with insulating barriers and demonstrate that these effects may qualitatively modify the Josephson current in such structures. We also investigate an impact of the parity effect on persistent currents in superconducting nanorings interrupted by a quantum point contact (QPC). In the limit of zero temperature and for the odd number of electrons in the ring we predict complete suppression of the supercurrent across QPC with one conducting mode. In nanorings with SNS junctions a p-state can occur for the odd number of electrons. Changing this number from even to odd yields spontaneous supercurrent in the ground state of such rings without any externally applied magnetic flux. where f is the difference between the phases of the BCS order parameters of two superconductors. Equation (1) represents the dc Josephson effect. The answer to the Einstein's question [1] turned out to be positive.What if the total current I flowing through the barrier is larger than I c ? In this case a part of the net current across the barrier is transferred by normal electrons (quasiparticles) and the rest of it is carried by Cooper pairs. While the second contribution, I s , remains dissipativeless and is again described by Eq. (1), the first -quasiparticle -contribution to the current is dissipative and, hence, causes a nonzero voltage drop V across the insulating barrier. In the presence of this voltage the coherent phase difference f acquires a time dependence described by another famous Josephson relation ¶fCombining Eqs. (1) and (2) one immediately arrives at the conclusion that for any nonzero V the supercurrent I s changes in time. In the case of time-independent voltages one has f = 2eVt/h and, hence, the Josephson current (1) will oscillate in time with the fundamental frequency proportional to the voltage V. Equation (2) and related to it oscillations of the supercurrent represent the essence of the ac Josephson effect. Soon after these Josephson's predictions the microscopic theory of both dc [3] and ac [4,5] was constructed and these effects have been observed experimentally [6,7]. Huge number of publications as well as several monographs are devoted to various aspects of these effects. It turned out that physics encoded in these phenomena is very rich and important for understanding of basic properties of superconductivity it-

Josephson current through a molecular transistor in a dissipative environment

“…This so-called π junction behavior, which is consequently also relevant in the Kondo regime, has been studied in a number of papers. [5][6][7][8][9][10][11] For larger dots the interplay of the above mentioned parity effect and the Josephson effect has also been addressed. 12 Experimentally, there has been a number of studies of metallic wires connected to superconductors, 13,14 but only a few studies in the Coulomb blockade regime.…”

Spontaneous Josephson π junctions with topological superconductors

“…To analyze H Latt , we first rewrite it in a Bogoliubov-de Gennes form, H Latt = 1 2 nn ψ † n H nn ψ n , where ψ † n = (c † n , c T n ), and accordingly H nn is a 4 × 4 matrix that includes spin and particle-hole degrees of freedom. The (8,9)]. Each of the superconductors is of length Lsc = 100a0.…”

“…Josephson π-junctions have been studied extensively in recent decades [1][2][3][4][5][6][7][8][9]. Unlike the more common Josephson 0-junctions, where the free energy is minimized by a phase difference of φ = 0, these are junctions in which the free energy is minimized by a phase difference of φ = π.…”

“…An important question is whether a π junction can spontaneously form, in the absence of magnetic fields, in a junction between two topological superconductors. In the case of trivial superconductors, it has been established that a superconductor -quantum dot -superconductor (S-QD-S) junction can exhibit π-junction behavior as a result of Coulomb interaction in the QD [8][9][10][11][12][13][14][15].…”

Josephson current through randomly oriented CNTs

“…The Josephson effect [1], as an observable quantum interference phenomenon in condensed matter physics has attracted a great deal of theoretical [2][3][4][5][6][7][8][9][10][11] and experimental [12][13][14][15][16][17][18] attention: A dissipation-less flow of Cooper pairs between two weakly coupled superconductors separated by a thin intermediate region with arbitrary quantum ground state is possible, provided the supercurrent does not exceed some threshold. This critical current density depends on the ground and low-lying excited states and geometry of the intermediate material.…”