Anomalous Hall effect in Weyl superconductors

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.

8 pages, 1 figure, published version. Invited article for the Focus Issue on Topological Semimetals

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Cited by in corpus (7)

• Weyl Metals
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Proximity-Induced Superconductivity with Subgap Anomaly in Type II Weyl Semi-Metal WTe2
• Thin film of a topological insulator as a spin Hall insulator
• Antiferromagnetism and spin density waves in 3D Dirac semimetals
• Symmetries of Weyl Superconductors with Different Pairings
• Collective Modes in Weyl Superconductors and the Axial Anomaly