Genesis and fading away of persistent currents in a Corbino disk geometry

TL;DR

This paper provides a comprehensive analytical and numerical study of persistent currents in a Corbino disk geometry, exploring their emergence, decay, and dependence on geometric parameters, with implications for experimental interpretation.

Contribution

It introduces a general expression for persistent currents in narrow annuli, extending analysis to multi-channel wide annuli, and confirms results with the Byers-Yang formula.

Findings

Derived a general expression for persistent currents in narrow annuli.

Confirmed analytical results with numerical simulations and the Byers-Yang formula.

Analyzed the evolution of persistent currents from nanodot to macroscopic scales.

Abstract

The detailed analytical and numerical analysis of the electron spectrum, persistent currents, and their densities for an annulus placed in a constant magnetic field (Corbino disk geometry) is presented. We calculate the current density profiles and study their dependence on the inner and outer radii of the annular. We study evolution of the persistent currents and track their emergence and decay for different limiting cases of such a geometry, starting from a nanodot and ending by a macroscopic circle. Our analytical results for the currents are confirmed by the agreement between the integration of the corresponding current densities and the application of the Byers-Yang formula, when it is applicable. Among other results we find the general expression for the persistent current in a narrow annulus, which in the one channel approximation reproduces the well-known result for quasi-one dimensional mesoscopic metallic ring. Moreover it allows to analyze the multi-channel case of a relatively wide annulus. Our study can be used for more accurate treatment and interpretation of the experimental data with measurements of the persistent currents in different doubly-connected systems.