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

TL;DR

This paper develops a microscopic theory explaining the zero-field superconducting diode effect in twisted trilayer graphene with WSe2, highlighting the role of spin-orbit coupling, pairing instabilities, and doping-dependent sign changes.

Contribution

It provides a detailed theoretical framework for the superconducting diode effect in twisted trilayer graphene, including classification of pairing states and explanation of experimental observations.

Findings

Diode effect arises from specific pairing instabilities and normal-state orders.

The sign change of current asymmetry with doping is explained by approximate chiral symmetry.

The theory links the diode effect to finite-momentum pairing and spin-orbit coupling.

Abstract

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