Self-doped Crystal from Preempted Band-inversion Transitions

Abstract

Recent experiments in rhombohedral graphene find evidence for a "self-doped" Wigner crystal (SDC) in which a slightly incommensurate Wigner crystal (WC) coexists with a small Fermi sea. We provide non-perturbative arguments that such SDCs generically arise from preempted band-inversion transitions between commensurate crystals, which motivates simple band-theory criteria for their appearance. Self-consistent Hartree-Fock calculations establish the existence of a SDC consistent with this mechanism in both the $\lambda$-jellium model and rhombohedral pentalayer graphene (R5G). In the $\lambda$-jellium model, we identify a SDC phase located between a "halo"-WC and an anomalous Hall crystal (AHC), which would otherwise be connected via a Dirac transition when pinned to commensuration; this contrasts with the WC-AHC transition, which we show cannot be connected by a continuous transition due to a mismatch of symmetry indices. In R5G, we predict a SDC phase located between a WC and a "disqualified" halo anomalous Hall crystal. We discuss in general how the Berry curvature distribution in the parent band affects the appearance of SDC, revealing a novel role of quantum geometry in inducing exotic quantum phases of matter.