Re-entrant Superconductivity Through a Quantum Lifshitz Transition in Twisted Trilayer Graphene

A series of recent experiments has demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. (arxiv:2103.12083) studies the behavior of the superconductor in an in-plane magnetic field and out-of-plane displacement field, finding that the superconductor is unlikely to be spin-singlet. This work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, it undergoes a transition to a distinct field-induced superconducting state. Inspired by this, we develop an understanding of the role that that an in-plane field plays in TTG, and use this understanding to argue that the transition may be associated with a quantum Lifshitz phase transition, with the high-field phase possessing finite-momentum pairing.