Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition

TL;DR

This paper investigates the critical behavior of two-dimensional disordered Dirac fermions and tests the conjecture that their transition shares universal properties with the integer quantum Hall transition, revealing discrepancies at zero energy.

Contribution

The study provides extensive numerical analysis of 2D disordered Dirac fermions in the unitary class, challenging the universality conjecture with new critical exponent results.

Findings

Critical line at m=0 with energy-dependent localization length exponent.

At large energies, results agree with known IQHT exponents (~2.56-2.62).

At zero energy, the exponent differs (~2.30-2.36), challenging the universality conjecture.

Abstract

Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig et al [Phys. Rev. B 50, 7526 (1994)] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. Here, we report the results of extensive numerics on the phase diagram and criticality of 2D-DDF in the unitary class. We find a critical line at m=0, with energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results \nu_IQH = 2.56 - 2.62 from models of the IQHT. At E=0 however, we obtain \nu_0 =2.30-2.36 incompatible with \nu_IQH. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.