Criticality of two-dimensional disordered Dirac fermions in the unitary class

Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics.
At E=0, Dirac fermions with mass m are band insulators,
with the Chern number jumping by unity at m=0. This observation motivated Ludwig et al. [Phys.
Rev. B 50, 7526] to suggest a relation between 2D disordered Dirac fermions (DDF) and
the integer quantum Hall transition (IQHT). They conjectured that the transitions in both systems
are controlled by the same fixed point and possess the same universal critical properties. Given the
far reaching implications for modern condensed matter physics and our understanding of disordered
critical points in general, it is surprising that the above conjecture has never been tested numerically.
Here, we report the results of extensive numerics on criticality and energy-mass phase diagram of
2D-DDF in the unitary symmetry 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 νIQH = 2.56–2.62 from models of the IQHT. At E=0 however, we
obtain ν0=2.30–2.36 incompatible with νIQH. Our result has practical importance for a variety of
experimental systems but also challenges conjectured relations between models of the IQHT.