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Two-dimensional (2D) Dirac fermions are a central paradigm of moderncondensed matter physics, describing low-energy excitations in graphene, incertain classes of superconductors, and on surfaces of 3D topologicalinsulators. 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 etal [Phys. Rev. B 50, 7526 (1994)] to conjecture that the transition in 2Ddisordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT)are controlled by the same fixed point and possess the same universal criticalproperties. Given the far-reaching implications for the emerging field of thequantum anomalous Hall effect, modern condensed matter physics and our generalunderstanding of disordered critical points, it is surprising that thisconjecture has never been tested numerically. Here, we report the results ofextensive numerics on the phase diagram and criticality of 2D-DDF in theunitary class. We find a critical line at m=0, with energy-dependentlocalization length exponent. At large energies, our results for the DDF areconsistent with state-of-the-art numerical results \nu_IQH = 2.56 - 2.62 frommodels of the IQHT. At E=0 however, we obtain \nu_0 =2.30-2.36 incompatiblewith \nu_IQH. This result challenges conjectured relations between differentmodels of the IQHT, and several interpretations are discussed.

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