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

References in corpus (15)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires
• Persistent currents in normal metal rings
• Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling
• Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect
• Majorana Fermions in Chiral Topological Ferromagnetic Nanowires
• Spin Orbit coupling and Anomalous Josephson effect in Nanowires
• Josephson Current through Semiconductor Nanowire with Spin-Orbit Interaction in Magnetic Field
• Screening Clouds and Majorana Fermions
• Enhanced Coherence of a Quantum Doublet Coupled to Tomonaga-Luttinger Liquid Leads
• $G_Q$-corrections in Circuit Theory of Quantum Transport
• Josephson current through a long quantum wire
• Boundary Field Theory Approach to the Renormalization of SQUID Devices
• The dc Josephson current in a long multi-channel quantum wire

Cited by in corpus (1)

• Persistent current in 2D topological superconductors