Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition

Sbierski, Björn; Dresselhaus, Elizabeth J.; Moore, Joel E.; Gruzberg, Ilya A.

doi:10.1103/physrevlett.126.076801

Title: Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition

Journal Article · Thu Feb 18 00:00:00 EST 2021 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.126.076801· OSTI ID:1822862

^[1];

^[1]; Moore, Joel E. ^[2];

^[3]

Univ. of California, Berkeley, CA (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
The Ohio State Univ., Columbus, OH (United States)

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)PRBMDO0163-182910.1103/PhysRevB.50.7526] 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. In this work, 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 an energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν_IQH=2.56-2.62 from models of the IQHT. At E=0, however, we obtain ν₀=2.30-2.36 incompatible with ν_IQH. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); German National Academy of Sciences; National Science Foundation (NSF)

Grant/Contract Number:: AC02-05CH11231; AC02-76SF00515; LPDS 2018-12; DGE-1752814

OSTI ID:: 1822862

Journal Information:: Physical Review Letters, Vol. 126, Issue 7; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition

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