Non-Abelian spin Hall insulator

TL;DR

This paper explores the theoretical possibility of realizing a non-Abelian spin Hall insulator, a topologically ordered state, in twisted MoTe2, highlighting the conditions under which it can be stabilized and its relation to experimental observations.

Contribution

It demonstrates that a non-Abelian spin Hall insulator can be stabilized at half filling in twisted MoTe2 by reducing opposite-spin interactions, providing a microscopic mechanism for this exotic phase.

Findings

A non-Abelian spin Hall insulator can be stabilized at half filling.

Band mixing can reduce opposite-spin interactions to favor this phase.

A small reduction in interactions can lead to a transition to a spin unpolarized phase.

Abstract

Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\rm MoTe}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall physics. We show that a non-Abelian spin Hall insulator, a state of two copies of the non-Abelian Moore-Read state, can be stabilized at half filling of time-reversal conjugate Chern bands. We elucidate that the existence of this phase relies on the reduction of opposite-spin interactions at short distances to overcome the Ising ferromagnetism. Moreover, we demonstrate that band mixing provides a generic mechanism for this reduction to be achieved. Quite remarkably, we find that a renormalization of opposite-spin interactions at short distances as small as 15 % of the moir\'e period is sufficient for a direct transition to a completely spin unpolarized phase which supports the non-Abelian spin Hall insulator. Furthermore, we show that the non-Abelian spin Hall insulator can either break time-reversal symmetry or preserve it depending on the underlying topological order.