Recent studies point to an exotic spin-triplet valley-singlet (STVS) superconducting phase in certain two-valley electron liquids, including rhombohedral trilayer graphene, Bernal bilayer graphene and ZrNCl, which nevertheless admits only trivial topology. Here, we predict that upon twisting two layers of STVS superconductors, a chiral $$f\pm {{{{{{{\rm{i}}}}}}}}{f}^{{\prime} }$$ f ± i f ′ -wave superconducting phase emerges near the ‘maximal’ twist angle of 30∘ where the system becomes an extrinsic quasi-crystal with 12-fold tiling. The resulting composite hosts an odd number of chiral Majorana edge modes and a single non-Abelian Majorana zero mode (MZM) in the vortex core. Through detailed symmetry analysis and microscopic modelling, we demonstrate that the non-Abelian topological superconductivity (TSC) forms robustly near the maximal twist when the isolated Fermi pockets coalesce into a single connected Fermi surface in the moiré Brillouin zone. Our results establish the large-twist-angle engineering, with distinct underlying moiré physics from magic-angle graphene, as a viable route toward non-Abelian TSC.
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.
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