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 ± if -wave superconductor -emerges in the vicinity of the 'maximal' twist angle of 30 • where the system becomes an extrinsic quasi-crystal with 12-fold tiling. The resulting composite is a non-Abelian topological superconductor with an odd number of chiral Majorana modes at its edges and a single Majorana zero mode (MZM) localized in the vortex core. As the twist angle deviates from 30 • , the system generically becomes a nodal f -wave topological superconductor supporting non-dispersive MZMs on the edge. Through symmetry analysis and detailed microscopic modelling based on a novel quasi-crystal band structure technique, we demonstrate that the chiral phase forms when the isolated Fermi pockets coalesce into a single connected Fermi surface around the center of the moiré Brillouin zone and is stable over a wide range of electron density. Our results thus establish a new platform for realizing, through twist angle engineering, an intrinsic chiral topological superconductor with non-Abelian excitations.