Higher-order topological superconductivity in twisted bilayer graphene

We show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. Multiple copies of C2zT-protected Majorana Kramers pairs appear at corners on pairing domain walls. The topology originates from the anomaly analyzed in Song et al. - the absence of a lattice support - of the single-valley band structure of twisted bilayer graphene, which is protected by C2zT and approximate particle-hole symmetry P. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, C2zT, and P must drive the system into a higher-order topological superconductor. Here spin-SU(2) is the global spin-SU(2) for the singlet pairing and is broken to U(1) for the triplet pairing. Using a Dirac Hamiltonian, we derive the corner modes and confirm with numerics. These corner states are stable even if P is weakly broken, which is true in experimental setups. Finally, we suggest experimental detection via the fractional Josephson effect in a TBG-TSC Josephson junction.