Josephson Diode Effect Induced by Valley Polarization in Twisted Bilayer Graphene

Recently, the Josephson diode effect (JDE), in which the superconducting critical current magnitudes differ when the currents flow in opposite directions, has attracted great interest. In particular, it was demonstrated that gate-defined Josephson junctions based on magic-angle twisted bilayer graphene showed a strong nonreciprocal effect when the weak-link region is gated to a correlated insulating state at half-filling (two holes per moir\'e cell). However, the mechanism behind such a phenomenon is not yet understood. In this work, we show that the interaction-driven valley polarization, together with the trigonal warping of the Fermi surface, induce the JDE. The valley polarization, which lifts the degeneracy of the states in the two valleys, induces a relative phase difference between the first and the second harmonics of supercurrent and results in the JDE. We further show that the nontrivial current phase relation, which is responsible for the JDE, also generates the asymmetric Shapiro steps.