Upper critical in-plane magnetic field in quasi-2D layered superconductors

TL;DR

This paper develops a theoretical framework to analyze the upper critical in-plane magnetic field in multilayer superconductors, applying it to recent graphene-based experiments and revealing potential g-factor enhancements.

Contribution

It introduces an analytically tractable model for the $H_{c2}$-$T_{c}$ relationship in multilayer superconductors considering spin-orbit coupling and depairing mechanisms.

Findings

The framework fits experimental data but suggests a discrepancy in spin-orbit parameters.

An enhancement of the Landé g factor may explain the discrepancy.

The model applies to both spin-singlet and spin-triplet pairing scenarios.

Abstract

The study of the interplay of applied external magnetic field and superconductivity has been invigorated by recent works on Bernal bilayer and rhombohedral multilayer 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. Here, we present a framework for analyzing the upper critical in-plane magnetic field data in multilayer superconductors. Our framework relies on an analytically tractable superconducting pairing model that captures the normal state phenomenology of these systems and applies it to calculate the relationship between the upper critical field $H_{c2}$ and the corresponding critical temperature $T_{c}$. We study the $H_{c2}-T_{c}$ 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 spin-triplet pairing. By applying our framework to analyze four recent Bernal bilayer graphene-WSe$_2$ experiments [1-4], we identify an apparent discrepancy between fitted and measured spin-orbit parameters, which we propose can be explained by an enhancement of the Land\'e g factor in the Bernal bilayer graphene experiments.