  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.
