Characteristic Potentials for Mesoscopic Rings Threaded by an Aharonov-Bohm Flux

TL;DR

This paper explores how Aharonov-Bohm flux influences electro-static potentials and persistent currents in mesoscopic rings, introducing characteristic functions to describe flux-dependent potential variations and capacitances.

Contribution

It introduces a model linking flux-sensitive electro-static potentials to persistent currents and flux-induced capacitance in mesoscopic rings, highlighting flux effects on electro-static properties.

Findings

Flux-sensitive potential leads to enhanced persistent currents.

Flux induces a measurable capacitance related to charge variation.

Characteristic functions describe potential changes due to external parameters.

Abstract

Electro-static potentials for samples with the topology of a ring and penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the electron-density distribution to small variations in the flux generates an effective electro-static potential which is itself a periodic function of flux. We investigate a simple model in which the flux sensitive potential leads to a persistent current which is enhanced compared to that of a loop of non-interacting electrons. For sample geometries with contacts the sensitivity of the electro-static potential to flux leads to a flux-induced capacitance. This capacitance gives the variation in charge due to an increment in flux. The flux-induced capacitance is contrasted with the electro-chemical capacitance which gives the variation in charge due to an increment in an electro-chemical potential. The discussion is formulated in terms of characteristic functions which give the variation of the electro-static potential in the interior of the conductor due to an increment in the external control parameters (flux, electro-chemical potentials). Paper submitted to the 16th Nordic Semiconductor Meeting, Laugarvatan, Iceland, June 12-15, 1994. The proceedings will be published in Physica Scripta.