Pairing symmetry of interacting fermions on twisted bilayer graphene superlattice

TL;DR

This study uses quantum Monte Carlo simulations to investigate the pairing symmetry in twisted bilayer graphene, revealing dominant d-wave pairing and potential for topological superconductivity with gapless edge states.

Contribution

It demonstrates the dominant pairing channels and topological nature of the superconducting phase in a realistic model of twisted bilayer graphene.

Findings

Dominant d-wave pairing symmetry identified.

Potential for topological $d_{x^2-y^2}+id_{xy}$ superconducting phase.

Insulating behavior at half-filling even with weak interactions.

Abstract

The pairing symmetry of an effective Hamiltonian for interacting fermions on a twisted bilayer graphene superlattice is studied with the determinant quantum Monte Carlo method. The model has the symmetry of a triangle lattice and a nearly-flat low energy band, features which underlie the magic-angle twisted bilayer graphene superlattice. We show that the low temperature phase is insulating at half-filling, even for relatively weak interactions. The natures of the spin and pairing correlations upon doping are determined, and exhibit an electron-hole asymmetry consistent with experiment. Among the pairing symmetries allowed, we demonstrate that the dominating channels are $d$-wave, opening the possibility of condensation into an unconventional $d_{x^2-y^2}+id_{xy}$ phase, which is characterized by an integer topological invariant and gapless edge states.