Upper critical in-plane magnetic field in layered graphene superconductors

The interplay of applied external magnetic field and superconductivity has been invigorated by recent works on Bernal bilayer and rhombohedral graphene. These studies, with and without proximitized spin-orbit coupling, have opened up a new frontier in the exploration of unconventional superconductors as they offer a unique platform to investigate superconductivity with high degree of in-plane magnetic field resilience and even magnetic field-induced superconductivity. We present a framework for an analytically tractable superconducting pairing model that captures the normal state phenomenology of these systems and apply it to calculate the relationship between the upper critical field $B_{c2}$ and the corresponding critical temperature $T_{c}$. We study the $B_{c2}-T_{c}$ critical curve as a function of experimental parameters (Ising and Rashba spin-orbit coupling) and depairing mechanisms (Zeeman and orbital coupling) for both spin-singlet and triplet pairing. Applying our framework to analyze four recent Bernal bilayer graphene-WSe$_2$ experiments, we identify an apparent discrepancy between fitted and measured spin-orbit parameters, which we propose can be explained by an enhancement of the Landé g factor in the Bernal bilayer graphene experiments.