Dirac electrons in graphene have a valley degree of freedom that is being explored as a carrier of information. In that context of "valleytronics" one seeks to coherently manipulate the valley index. Here we show that reflection from a superlattice potential can provide a valley switch: Electrons approaching a pristine-graphene-superlattice-graphene interface near normal incidence are reflected in the opposite valley. We identify the topological origin of this valley switch, by mapping the problem onto that of Andreev reflection from a topological superconductor, with the electron-hole degree of freedom playing the role of the valley index. The valley switch is ideal at a symmetry point of the superlattice potential, but remains close to 100% in a broad parameter range.

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 ¼ 0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m ¼ 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 ¼ 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 ¼ 2.56-2.62 from models of the IQHT. At E ¼ 0, however, we obtain ν 0 ¼ 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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