Universal Conductance Distribution in the Quantum Size Regime

TL;DR

This paper investigates the universal conductance distribution in isolated quantum rings within the discrete spectrum limit, revealing a power-law behavior influenced by symmetry properties, with implications for high moments of conductance.

Contribution

It introduces a universal conductance distribution function in the quantum size regime, highlighting the role of symmetry and the distribution's tail in determining conductance moments.

Findings

Distribution follows a power-law P(g)~g^{-(4+β)/3}

Universal behavior observed across a range of conductance values

High moments are dominated by the nonuniversal tail

Abstract

We study the conductance (g) distribution function of an ensemble of isolated conducting rings, with an Aharonov--Bohm flux. This is done in the discrete spectrum limit, i.e., when the inelastic rate, frequency and temperature are all smaller than the mean level spacing. Over a wide range of g the distribution function exhibits universal behavior P(g)\sim g^{-(4+\beta)/3}, where \beta=1 (2) for systems with (without) a time reversal symmetry. The nonuniversal large g tail of this distribution determines the values of high moments.