Resonating-valence-bond superconductor from small Fermi surface in twisted bilayer graphene

Abstract

Mechanism of superconductivity in twisted bilayer graphene (TBG) remains one of the central problems in correlated moir\'e materials. The most intriguing question is about the nature of the normal state: is the Cooper pair formed from small Fermi surface or large Fermi surface? In this work we point out the possibility of a symmetric pseudogap metal with small hole pockets, dubbed as second Fermi liquid (sFL). In the sFL phase at $\nu=-2-x$, there is a two-component picture: two electrons mainly localize at each AA site and form a paired singlet due to anti-Hund's coupling mediated by the optical phonon, while additional holes doped into the AA sites form small Fermi surfaces. The sFL phase corresponds to an intrinsically strongly interacting fixed point and is topologically distinct to the conventional Fermi liquid. We develop a unified framework to describe both a renormalized FL phase and an sFL phase. We propose that the TBG superconductor emerges from the sFL phase, but is close to the transition toward the FL phase under increasing hole doping. In the superconductor, pairing of local moments is shared to the mobile carriers and a smaller superconducting gap with nodal $p_x$ symmetry is opened on the small hole pockets. This work provides, to our knowledge, the first unified theory that explains both the pseudogap metal above $T_c$ and the two-gap nematic superconductivity below it.