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

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.