Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition

TL;DR

This paper reveals that conductance fluctuations in a quantum Hall system exhibit a universal resonance linked to topological quantum number changes, enabling new insights into the critical behavior of phase transitions.

Contribution

It introduces a novel universal feature in mesoscopic conductance fluctuations that directly relates to topological quantum number changes at the quantum Hall transition.

Findings

Identification of a universal magnetoconductance resonance

Resonance signals a change in topological quantum number

Provides a new signed scaling variable for critical exponent

Abstract

The conductance of a two-dimensional electron gas at the transition from one quantum Hall plateau to the next has sample-specific fluctuations as a function of magnetic field and Fermi energy. Here we identify a universal feature of these mesoscopic fluctuations in a Corbino geometry: The amplitude of the magnetoconductance oscillations has an e^2/h resonance in the transition region, signaling a change in the topological quantum number of the insulating bulk. This resonance provides a signed scaling variable for the critical exponent of the phase transition (distinct from existing positive definite scaling variables).