Filling- and interaction-modulated pairing symmetry in twisted bilayer graphene

Abstract

Superconductivity in twisted bilayer graphene has attracted much attention in recent years. Based on the significant experimental facts, there are many theoretical investigations on its superconducting mechanism and pairing symmetry. In this paper, we study the theory of the electron-phonon coupling in magic-angle twisted bilayer graphene starting from the work of Lian et al. [Phys. Rev. Lett. 122, 257002 (2019)] and thereby develop a uniform framework for the low as well as high electron densities. From this beneficial approach, we obtain the strongest superconductivity near the moir\'e band filling factor $|\ensuremath{\nu}|\ensuremath{\approx}2$, consistent with the experimental results. By associating it with the Coulomb interaction, we find that the pairing symmetry is strongly dependent on the filling factor, with the $p$-wave, $f$-wave, and $s$-wave pairing states sequentially appearing. It can be confirmed that the superconductivity mostly exists near the half filling of the lowest flat bands with an $f$-wave pairing symmetry. We discuss the possible origin of these phenomena, the stability of the superconductivity, and also the feasible experimental verification.