Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors

The robustness against local perturbations, as long as the symmetry of the system is preserved, is a distinctive feature of topological quantum states. Magnetic impurities and defects break time-reversal invariance and, consequently, time-reversal invariant (TRI) topological superconductors are fragile against this type of disorder. Non-magnetic impurities, however, preserve time-reversal symmetry and one naively expects a TRI topological superconductor to persist in the presence of non-magnetic impurities. In this work, we study the effect of non-magnetic disorder on a TRI topological superconductor with extended $s$-wave pairing, which can be engineered at the interface of an Fe-based superconductor and a strongly spin-orbit coupled Rashba layer. We model two different types of non-magnetic random disorder and analyze both the bulk density of states and edge state spectrum. Contrary to naive expectations, we find that the disorder strongly affects the topological phase by closing the energy gap, while trivial superconducting phases remain stable and fully gapped. The disorder phase diagram reveals a strong expansion of a nodal phase with increasing disorder. We further show the decay of the helical Majorana edge states in the topological phase and how they eventually disappear with increasing disorder. These results alter our understanding of effects of impurities and disorder on TRI topological phases and may help explain the difficulty of experimental observation of TRI topological superconductors.Comment: 8 pages, 7 figure

Nematic superconductivity in magic-angle twisted bilayer graphene from atomistic modeling

Bilayer graphene with small internal twist angles develops large scale moir\'e patterns with flat energy bands hosting both correlated insulating states and superconductivity. The large system size and intricate band structure have however hampered investigations into the properties of the superconducting state. Here, we use full-scale atomistic modeling with local electronic interactions and find a highly inhomogeneous superconducting state with nematic ordering on both the atomic and moir\'e lattice length scales. More specifically, we obtain locally anisotropic real-valued d-wave pairing with a nematic vector winding throughout the moir\'e pattern, generating a three-fold ground state degeneracy. Despite the d-wave nature, the superconducting state has a full energy gap, which we further tie to a {\pi}-phase interlayer coupling. The superconducting nematicity is easily detected through signatures in the local density of states. Our results show not only that atomistic modeling is essential for twisted bilayer graphene but also that the superconducting state is necessarily distinctly different from that of the high-temperature cuprate superconductors, despite similarity in electronic interactions.Comment: 4 figure