Minigap, Parity Effect and Persistent Currents in SNS Nanorings

TL;DR

This paper investigates the effects of impurities, magnetic flux, and supercurrents on the energy spectrum and persistent currents in SNS nanorings, revealing tunable minigaps and novel current-phase relations.

Contribution

It provides a comprehensive analysis of the proximity-induced minigap and persistent currents in SNS nanorings with arbitrary impurity concentrations, including the discovery of non-monotonous flux dependence and $ ext{pi}$-junction states.

Findings

Minigap opens at weak disorder and can be tuned by supercurrent or magnetic flux.

Non-monotonous minigap dependence on flux at weak disorder.

Odd-electron nanorings exhibit $ ext{pi}$-junction behavior and spontaneous currents.

Abstract

We have evaluated a proximity-induced minigap in the density of states (DOS) of SNS junctions and SNS nanorings at an arbitrary concentration of non-magnetic impurities. We have demonstrated that an isotropic energy minigap in the electron spectrum opens up already at arbitrarily weak disorder, while angle resolved DOS at higher energies can remain strongly anisotropic. The minigap value $\epsilon_g$ can be tuned by passing a supercurrent through an SNS junction or by applying a magnetic flux $\Phi$ to an SNS ring. A non-monotonous dependence of $\epsilon_g$ on $\Phi$ has been found at weak disorder. We have also studied persistent currents in isolated SNS nanorings. For odd number of electrons in the ring we have found a non-trivial current-phase (current-flux) relation which -- at relatively high disorder -- may lead to a $\pi$-junction state and spontaneous currents in the ground state of the system.