Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors

Abstract

Recent theoretical and experimental studies point to a novel spin-triplet valley-singlet (STVS) superconducting phase in certain two-valley electron liquids, including rhombohedral trilayer graphene, Bernal bilayer graphene and ZrNCl. This fully gapped phase is exotic in that it combines into Cooper pairs same-spin electrons from valleys centered around the opposing corners of a hexagonal Brillouin zone, but is, nevertheless, topologically trivial. Here, we predict that upon stacking two layers of an STVS material with an angular twist, a novel chiral topological phase -- an $f \pm if'$-wave superconductor -- emerges in the vicinity of the `maximal' twist angle of 30$^{\circ}$ where the system becomes an extrinsic quasi-crystal with 12-fold tiling. The resulting composite is a non-Abelian topological superconductor (TSC) with an odd number of chiral Majorana modes at its edges and a single Majorana zero mode (MZM) localized in the vortex core. Through symmetry analysis and detailed microscopic modelling based on a novel quasi-crystal band structure technique, we demonstrate that the non-Abelian TSC forms when the isolated Fermi pockets coalesce into a single connected Fermi surface around the center of the moir\'{e} Brillouin zone and is stable over a wide range of electron density. We further discuss how the energetics leading to the $f \pm if'$-wave phase results in anomalous $\pi$-periodic inter-layer Josephson effect, which can serve as a distinctive signature of the chiral phase. Distinct from the valley-preserving moir\'{e} physics in small-angle twisted graphene, our results establish the large-angle moir\'{e} physics arising near maximal twist as a new avenue toward intrinsic TSC with non-Abelian excitations.