Topological superconductivity with emergent vortex lattice in twisted semiconductors

TL;DR

This paper predicts a topological chiral f-wave superconducting state with a vortex lattice in twisted semiconductors, linking fractional quantum anomalous Hall effects to emergent magnetic fields and topological superconductivity.

Contribution

It introduces a novel topological superconducting phase with double vortices and half-integer Chern number in twisted semiconductors, unifying FQAH and topological superconductivity mechanisms.

Findings

Superconducting state hosts double vortices induced by emergent magnetic field.

The vortex lattice state is topological with Chern number -1/2.

Features a half-integer thermal Hall conductance.

Abstract

The coexistence of superconductivity and fractional quantum anomalous Hall (FQAH) effect has recently been observed in twisted MoTe$_2$ and theoretically demonstrated in a model of repulsively interacting electrons under an emergent magnetic field arising from the layer pseudospin texture in moir\'e superlattice. Here, we show that this superconducting state is a chiral $f$-wave superconductor hosting an array of $double$ vortices, which are induced by the emergent magnetic field with $h/e$ flux quanta per moir\'e unit cell. This superconducting vortex lattice state is topological and features Chern number $-1/2$, giving rise to a half-integer thermal Hall conductance. Our theory provides a common mechanism and unified understanding of FQAH and topological superconductivity, with a rich phase diagram controlled by the spatial modulation of the emergent magnetic field.