Reentrant superconductivity enabled by spin-orbit coupling: Application to UTe$_2$

Abstract: Reentrant superconductivity has been understood primarily in terms of the Jaccarino-Peter field-compensation effect or from a change of the strength in the pairing interaction. However, neither mechanism appears able to entirely explain the remarkable phase diagram of UTe$2$. Here we propose a generic theory of the field-enhancement of opposite-spin Cooper pairings which does not necessitate the coexistence of magnetism or the vicinity of a magnetic quantum critical point. Our analytical treatment shows that the reentrance has its origin in the interplay of the sublattice degrees of freedom and spin-orbit coupling, which can can strikingly enhance opposite-spin Cooper pairings at strong Zeeman fields. Based on these results, we show that a pairing state with B${3u}$ symmetry can reproduce the highly anisotropic phase diagram of the reentrant superconducting state of UTe$_2$.