Loop currents and anomalous Hall effect from time-reversal symmetry-breaking superconductivity on the honeycomb lattice

TL;DR

This paper demonstrates that chiral superconductivity on the honeycomb lattice can induce loop currents and an anomalous Hall effect, revealing a topological mass gap and Kerr effect without external magnetic fields.

Contribution

It introduces a gauge-invariant time-reversal-odd bilinear in chiral superconductors on the honeycomb lattice, linking sublattice polarization to topological phenomena.

Findings

Loop currents arise around lattice sites due to pairing bilinear.

A topological mass gap at Dirac points leads to anomalous Hall conductivity.

Presence of Kerr effect without external magnetic field.

Abstract

We study a tight-binding model on the honeycomb lattice of chiral $d$-wave superconductivity that breaks time-reversal symmetry. Due to its nontrivial sublattice structure, we show that it is possible to construct a gauge-invariant time-reversal-odd bilinear of the pairing potential. The existence of this bilinear reflects the sublattice polarization of the pairing state. We show that it generates persistent loop current correlations around each lattice site and opens a topological mass gap at the Dirac points, resembling Haldane's model of the anomalous quantum Hall effect. In addition to the usual chiral $d$-wave edge states, there also exist electron-like edge resonances due to the topological mass gap. We show that the presence of loop-current correlations directly leads to a nonzero intrinsic ac Hall conductivity, which produces the polar Kerr effect without an external magnetic field. Similar results also hold for the nearest-neighbor chiral $p$-wave pairing. We briefly discuss the relevance of our results to superconductivity in twisted bilayer graphene.