Higher-order topological superconductivity in twisted bilayer graphene
In this work, we show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. Multiple copies of C 2z T-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 C 2z T and approximate particle-hole symmetry $\mathcal{P}$. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, C 2z T, and $\mathcal{P}$ 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 $\mathcal{P}$ 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.