Is There a Magnetic-Field-Induced Breakdown in the Universality of Conductance Fluctuations?

Abstract

Over the past few years, there have been many reports of the breakdown of universality in conductance fluctuations in mesoscopic systems when a high magnetic field is applied, particularly in the case of quantum wires. Normally, conductance fluctuations are described by a single scaling parameter–the coherence length lφ. The increase in the magnetic coherence length B c is generally attributed to a decrease in lφ which is not observed in the amplitude of the fluctuations. Worse, in high mobility material, the fluctuations seem to increase in amplitude, which is also inconsistent with a decrease in lφ. Here, we argue that (1) the wire behavior is governed by surface scattering, (2) there is a formation of edge states in the high magnetic field, and (3) a breakdown of diffusive transport and transition to quasi-ballistic transport in the edge states in high-mobility material. The transition to high field behavior occurs when the cyclotron orbit at the Fermi surface becomes smaller than the width, so that proper treatment of the amplitude of the fluctuations and of the magnetic correlation length remains in keeping with theoretically expected behavior without loss of universality.