Aharonov-Bohm effect in one-channel weakly disordered rings

TL;DR

This paper introduces a new diagrammatic method to analyze the density of states in a weakly disordered one-channel ring threaded by magnetic flux, revealing oscillations with flux quantum and a transition from weak localization to ballistic regime.

Contribution

A novel diagrammatic approach reformulating Berezinskii's technique to exactly compute the density of states in disordered rings with magnetic flux.

Findings

Density of states oscillates with flux quantum φ₀.

Transition from weak localization to ballistic regime as sample length decreases.

Exact dependence of density of states on ring size and disorder strength.

Abstract

A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states $\rho(\epsilon,\phi)$ of a one-channel weakly disordered ring, threaded by an external magnetic flux. The exact result obtained for the density of states shows an oscillation of $\rho(\epsilon,\phi)$ with a period of the flux quantum $\phi_0= hc/e $. As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime (L >> l) to the ballistic one (L <= l). The analytical expression for the density of states shows the exact dependence of $\rho(\epsilon,\phi)$ on the ring's circumference and on disorder strength for both regimes.