The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law

TL;DR

This paper explores how emergent modular symmetries influence the quantum Hall effect in graphene, offering new predictions for plateau locations, transition points, and conductivities, which align well with experimental data.

Contribution

It introduces a novel application of modular symmetry concepts to graphene's quantum Hall effect, deriving specific testable predictions distinct from traditional semiconductor systems.

Findings

Predicted locations of quantum Hall plateaux in graphene.

Identified critical points and transition rules between plateaux.

Observed semi-circle law in conductivity transitions.

Abstract

Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed quantum Hall effect in graphene as a test of these ideas, and identify to this end a class of predictions for graphene which would follow from the same modular arguments. We are led to a suite of predictions for high mobility samples that differs from those obtained for the conventional quantum Hall effect in semiconductors, including: predictions for the locations of the quantum Hall plateaux; predictions for the positions of critical points on transitions between plateaux; a selection rule for which plateaux can be connected by low-temperature transitions; and a semi-circle law for conductivities traversed during these transitions. Many of these predictions appear to provide a good description of graphene measurements performed with intermediate-strength magnetic fields.