Universal Fluctuation of the Hall Conductance in the Random Magnetic Field

TL;DR

This paper demonstrates that the root mean square fluctuation of the antisymmetric Hall conductance in a mesoscopic metal with a random magnetic field is universally of order e^2/h, regardless of field strength, revealing new insights into T-symmetry breaking systems.

Contribution

It establishes the universality of Hall conductance fluctuations in random magnetic fields and proposes an experimental approach to observe this effect.

Findings

RMS fluctuation of Hall conductance is universal and of order e^2/h.

Fluctuation is independent of magnetic field amplitude and diffusion coefficient.

The effect is zero in systems with only scalar disorder.

Abstract

We show that the RMS fluctuation of the antisymmetric part of the Hall conductance of a planar mesoscopic metal in a random magnetic field with zero average is universal, of the order of $e^2/h$, independent of the amplitude of the random magnetic field and the diffusion coefficient even in the weak field limit. This quantity is exactly zero in the case of ordinary scalar disorder. We propose an experiment to measure this surprising effect, and also discuss its implications on the localization physics of this system. Our result applies to some other systems with broken time-reversal ({\bf T}) symmetry.