Non-Abelian spin Hall insulator

Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>MoTe</a:mi><a:mn>2</a:mn></a:msub></a:math>, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall physics. We show that a 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 moiré period is sufficient for a 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.