  We investigate superconducting pairing tendencies of a two-dimensional
electron fluid with both valley and spin degrees of freedom, both without and
in the presence of an in-plane magnetic field. We present suggestive
theoretical arguments that spontaneous valley polarization can lead to exotic
singlet superconducting tendencies, including pair-density-wave order at zero
field and re-entrant superconductivity at high field. We also find a reduced
magnetic response in the polarized valley, which allows a finite violation of
the Pauli limit. These results are obtained by a mean-field approach to a
generalized $t$-$J$ model on a triangular lattice and in the dilute limit.
Phenomenological similarities to results of recent magic-angle twisted trilayer
graphene experiments are noted.
