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arXiv · 1605.05734

Anomalous Hall effect in Weyl superconductors

G. Bednik·A. A. Zyuzin·A. A. Burkov
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Abstract

We present a theory of the anomalous Hall effect in a topological Weyl superconductor with broken time reversal symmetry. Specifically, we consider a ferromagnetic Weyl metal with two Weyl nodes of opposite chirality near the Fermi energy. In the presence of inversion symmetry, such a metal experiences a weak-coupling Bardeen-Cooper-Schrieffer (BCS) instability, with pairing of parity-related eigenstates. Due to the nonzero topological charge, carried by the Weyl nodes, such a superconductor is necessarily topologically nontrivial, with Majorana surface states coexisting with the Fermi arcs of the normal Weyl metal. We demonstrate that, surprisingly, the anomalous Hall conductivity of such a superconducting Weyl metal coincides with that of a nonsuperconducting one, under certain conditions, in spite of the nonconservation of charge in a superconductor. We relate this to the existence of an extra (nearly) conserved quantity in a Weyl metal, the chiral charge.

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G. Bednik, A. A. Zyuzin, A. A. Burkov. 2016-08-22. Anomalous Hall effect in Weyl superconductors. https://doi.org/10.1088/1367-2630%2F18%2F8%2F085002

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