Theory of zero-field superconducting diode effect in twisted trilayer graphene

In a recent experiment [Lin et al., arXiv:2112.07841], the superconducting phase hosted by heterostructure of mirror-symmetric twisted trilayer graphene and WSe$_2$ was shown to exhibit significantly different critical currents in opposite directions absence external magnetic fields. We here develop microscopic theory analyze necessary conditions for this zero-field diode effect. Taking into account spin-orbit coupling induced via proximity effect, we classify pairing instabilities normal-state orders derive which combinations are consistent with observed particular, its field trainability. perform explicit calculations effect several models, including full continuum model system, illuminate relation between finite-momentum pairing. Our also provides natural explanation sign change current asymmetry doping, can be related an approximate chiral symmetry enhanced transverse resistance above transition. findings not only elucidate rich physics on WSe$_2$, but establish means distinguish various candidate interaction-induced spin-orbit-coupled moir\'e systems, could therefore serve as guide future experiments well.