Transfer matrix approach to the persistent current in hybrid normal-superconducting rings

Abstract

Using the properties of the transfer matrix of one-dimensional quantum mechanical systems, we derive a technique to exactly compute the persistent current across a hybrid normal-superconducting-mesoscopic ring pierced by a magnetic flux Phi as a single integral of a known function of the system's parameters. Our approach provides exact results at zero temperature, which can be readily extended to finite temperatures T much below the superconducting gap. We apply our technique to derive the persistent current through p-wave and s-wave superconducting-normal hybrid rings, recovering at once a number of effects such as the crossover in the current periodicity on increasing the size of the ring and the signature of the topological phase transition in the p-wave case. In the limit of a large ring size, resorting to a systematic expansion in inverse powers of the ring length, we derive exact analytic closed-form formulas, applicable to a number of cases of physical interest.

25 pages, 13 .eps figures

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• Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions
• Modifications of electron states, magnetization and persistent current in a quantum dot by controlled curvature
• Manipulation of Cooper pair entanglement in hybrid topological Josephson junctions
• Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains
• Probing Majorana zero modes by measuring transport through an interacting magnetic impurity
• Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field
• Out of equilibrium charge transport in molecular electronic devices
• Lifshitz transitions and Weyl semimetals from a topological superconductor with supercurrent flow
• Exactly solvable chain of interacting electrons with correlated hopping and pairing
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• Persistent current in 2D topological superconductors
• Phase transitions in quantum tunneling and quasi-exact solvability for a family of parametric double-well potentials