Metallic electron crystals in rhombohedral graphene as a bridge to twisted WSe$_2$

Abstract

Superconducting phases have recently been discovered both in twisted bilayers of transition metal dichalcogenide WSe$_2$ (tWSe$_2$) and in rhombohedral multilayer graphene (RMG). While both have generated extensive interest, they appear to be driven by qualitatively different physics. Here, we propose a unified picture in which the superconductivity in RMG arises from a strongly correlated metallic state with a spatial length scale that is compatible with the moiré length scale of tWSe$_2$. Central to this mechanism is a Wigner crystal phase in RMG that is metallic, driven by a "W"-shaped dispersion in the flat part of the underlying graphene band structure. We demonstrate this effect through calculations of Wigner crystal states in pentalayer RMG, focusing on dilute electrons in the quarter-metal regime relevant to experiment. In a region of the phase diagram we find the Wigner crystal breaks three-fold rotation symmetry, which guides our construction of a $t$-$V$ model on a triangular lattice as an effective description of the low-energy electronic physics. This construction suggests a surprisingly similar low-energy description of RMG and tWSe$_2$. Broader implications for superconductivity in dilute carrier systems are also discussed.