Origin of the anomalous Hall effect in two-band chiral superconductors

Abstract

We consider the origin of the anomalous Hall effect in a general model of a clean two-band chiral superconductor. Within the Kubo formalism we derive an analytic expression for the high-frequency ac Hall conductivity valid close to the critical temperature. This expression involves two distinct gauge-invariant time-reversal-odd bilinear (TROB) functions involving the pairing potential and its Hermitian conjugate. We argue that the existence of at least one of these TROBs generically implies a nonzero ac Hall conductivity. The TROBs allow us to clarify the roles of intra- and interband pairing, and provide a straightforward criterion for a superconducting state to exhibit the anomalous Hall effect. We briefly exemplify our results with model calculations for a chiral $p$-wave pairing state in strontium ruthenate and a chiral $d$-wave pairing state on the honeycomb lattice.

9 pages, 1 figure

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Cited by in corpus (12)

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• Anapole superconductivity from $\mathcal{P}\mathcal{T}$-symmetric mixed-parity interband pairing
• Quantum-geometry-induced anapole superconductivity
• General theory of robustness against disorder in multi-band superconductors
• Intrinsic Anomalous Hall Effect in a Bosonic Chiral Superfluid
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Quantum-geometry-induced anomalous Hall effect in nonunitary superconductors and application to Sr${}_2$RuO${}_4$
• Pair-breaking in superconductors with strong spin-orbit coupling
• Polar Kerr Effect in Multiband Spin-Orbit Coupled Superconductors
• Circular-polarization-selective perfect reflection from chiral superconductors
• Sensitivity of superconducting states to the impurity location in layered materials
• Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr${}_2$RuO${}_4$