Topological Superconductivity in Twisted Multilayer Graphene

We study a minimal Hubbard model for electronically driven superconductivity in a correlated flat miniband resulting from the superlattice modulation of a twisted graphene multilayer. The valley degree of freedom drastically modifies the nature of the preferred pairing states, favoring spin triplet $d+id$ order with a valley singlet structure. We identify two candidates in this class, which are both topological superconductors. These states support half-vortices carrying half the usual superconducting flux quantum $hc/(4e)$, and have topologically protected gapless edge states.

Figure 1

(a) The center of a unit cell of a bilayer graphene moiré superlattice, where Wannier states are peaked in the flat band. In this region there is AA stacking of the two layers, and coordinates referred to in the text are defined as shown. (b) Independent single-particle states are built from momenta near each of the two valleys shown as dark dots in the microscopic Brillouin zone corners, and these become the two orbitals in the Hubbard model of Eq. (1).

Figure 2

The virtual process in second order perturbation theory in $t/U$. An electron hops from the singly occupied site on the right to the one on the left, making it doubly occupied. The intermediate state may be (top) a spin triplet and orbital singlet or (bottom) a spin singlet and orbital triplet. The Hunds interaction favors the upper situation.