Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures

TL;DR

This paper provides a theoretical analysis of how magnetic fields cause a crossover from orthogonal to unitary symmetry in ballistic electron transport through chaotic microstructures, explaining experimental observations using random-matrix theory.

Contribution

It derives a universal expression for weak-localization correction in chaotic billiards, elucidating the symmetry crossover due to magnetic flux.

Findings

Universal formula for conductance correction depending on channels and flux

Quantitative description of symmetry crossover in chaotic systems

Theoretical explanation of experimental suppression of weak localization

Abstract

We study the ensemble-averaged conductance as a function of applied magnetic field for ballistic electron transport across few-channel microstructures constructed in the shape of classically chaotic billiards. We analyse the results of recent experiments, which show suppression of weak localization due to magnetic field, in the framework of random-matrix theory. By analysing a random-matrix Hamiltonian for the billiard-lead system with the aid of Landauer's formula and Efetov's supersymmetry technique, we derive a universal expression for the weak-localization contribution to the mean conductance that depends only on the number of channels and the magnetic flux. We consequently gain a theoretical understanding of the continuous crossover from orthogonal symmetry to unitary symmetry arising from the violation of time-reversal invariance for generic chaotic systems.