Superconductivity Proximate to Non-Abelian Fractional Spin Hall Insulator in Twisted Bilayer MoTe$_2$

Abstract

Twisted bilayer MoTe$_2$ near two-degree twists has emerged as a platform for exotic correlated topological phases, including ferromagnetism and a non-Abelian fractional spin Hall insulator. Here we reveal the unexpected emergence of an intervalley superconducting phase that intervenes between these two states in the half-filled second moiré bands. Using a continuum model and exact diagonalization, we identify superconductivity through multiple signatures: negative binding energy, a dominant pair-density eigenvalue, finite superfluid stiffness, and pairing symmetry consistent with a time-reversal-symmetric nodal extended $s$-wave state. Remarkably, our numerical calculation suggests a continuous transition between superconductivity and the non-Abelian fractional spin Hall insulator, in which topology and symmetry evolve simultaneously, supported by an effective field-theory description. Notably, our field-theoretic analysis indicates that superconductivity is driven by the condensation of charge-$e/2$ self-bosonic non-Abelian anyons, thereby providing a concrete realization of anyon superconductivity. Complementarily, when approached from the normal metallic side, superconductivity instead emerges from a Kohn-Luttinger instability enabled by the non-uniform quantum geometry of the flat moiré bands. Our results establish higher moiré bands as fertile ground for intertwined superconductivity and topological order, and point to experimentally accessible routes for realizing superconductivity in twisted bilayer MoTe$_2$.