  A series of recent experiments have 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 these results, we develop an understanding of superconductivity in
TTG using a combination of phenomenological reasoning and microscopic theory.
We describe role that that an in-plane field plays in TTG, and use this
understanding to argue that the re-entrant transition may be associated with a
quantum Lifshitz phase transition, with the high-field phase possessing
finite-momentum pairing. We argue that the superconductor is likely to involve
a superposition of singlet singlet and triplet pairing, and describe the
structure of the normal state. We also draw lessons for twisted bilayer
graphene (TBG), and explain the differences in the phenomenology with TTG
despite their close microscopic relationship. We propose that a singlet-triplet
superposition is realized in the TBG superconductor as well, and that the $\nu
= -2$ correlated insulator may be a time reversal protected $\mathbb{Z}_2$
topological insulator obtained through spontaneous spin symmetry breaking.
