Identification of superconducting pairing symmetry in twisted bilayer graphene using in-plane magnetic field and strain

Abstract

We show how the pairing symmetry of superconducting states in twisted bilayer graphene can be experimentally identified by theoretically studying effects of externally applied in-plane magnetic field and strain. In the low field regime, superconducting critical temperature $T_c$ is suppressed by in-plane magnetic field $\boldsymbol{B}_{\parallel}$ in singlet channels, but is enhanced by weak $\boldsymbol{B}_{\parallel}$ in triplet channels, providing an important distinction. The in-plane angular dependence of the critical $\boldsymbol{B}_{\parallel, c}$ has a six-fold rotational symmetry, which is broken when strain is present. We show that anisotropy in $\boldsymbol{B}_{\parallel, c}$ generated by strain can be similar for $s$- and $d$-wave channels in moir\'e superlattices. The $d$-wave state is pinned to be nematic by strain and consequently gapless, which is distinguishable from the fully gapped $s$-wave state by scanning tunneling measurements.