Anomalous Hall effect in Weyl superconductors

TL;DR

This paper develops a theory for the anomalous Hall effect in Weyl superconductors with broken time reversal symmetry, showing that their Hall conductivity can match that of normal Weyl metals despite superconductivity.

Contribution

It introduces a theoretical framework for understanding the anomalous Hall effect in topological Weyl superconductors, highlighting the role of chiral charge conservation.

Findings

Hall conductivity in Weyl superconductors matches that of normal Weyl metals under certain conditions

Superconductivity does not alter the anomalous Hall effect due to chiral charge conservation

Weyl superconductors host Majorana surface states alongside Fermi arcs

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.