Higher-Order Topological Superconductivity in Twisted Bilayer Graphene

TL;DR

This paper demonstrates that twisted bilayer graphene with superconductivity can host higher-order topological phases featuring Majorana corner states and zero modes, protected by symmetries and originating from the system's anomaly.

Contribution

It proves that any compatible pairing in twisted bilayer graphene induces a higher-order topological superconductor phase, revealing new topological states and corner Majorana modes.

Findings

Presence of Majorana Kramers pairs at corners

Zero modes in Abrikosov vortices

Stability of corner states under weak symmetry breaking

Abstract

We show that introducing spin-singlet or spin-triplet superconductivity into twisted bilayer graphene induces higher-order topological superconductivity. $C_{2z}T$-protected corner states of Majorana Kramers pairs appear at the boundary between domains with opposite signs of pairing, and zero modes materialize in Abrikosov vortices. The topology of the superconducting phase originates from the anomaly [1] -- the absence of a lattice support -- of the single-valley band structure of twisted bilayer graphene, which is protected by $C_{2z}T$ and the particle-hole symmetry $\cal P$. We prove that any pairing (spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2), time-reversal, $C_{2z}T$, and $\cal P$ must drive the system into a higher-order topological superconductor phase. Here spin-SU(2) is the global spin-SU(2) for the singlet pairing and a combination of two SU(2)'s in the two valleys for the triplet pairing. Using a Dirac Hamiltonian, we demonstrate the existence of corner modes and confirm this with numerical calculations. These corner states are stable even if the approximate particle-hole symmetry $\cal P$ is weakly broken, which is true in experimental setups. Finally, we suggest an experiment to detect the topological superconductivity: by observing the fractional Josephson effect in a TBG-TSC Josephson system.