Crystals Caught Doping: Metallic Wigner Crystals in Rhombohedral Graphene

TL;DR

This paper develops a criterion for when commensurate Wigner crystals in rhombohedral graphene become metallic through self-doping, explaining recent experimental observations of conductance reversal.

Contribution

It introduces a general instability criterion for incommensurate Wigner crystals and applies it to rhombohedral graphene, revealing a broad metallic phase adjacent to insulating crystals.

Findings

Incommensurate Wigner crystals can spontaneously dope and become metallic.

The phase diagram shows a broad metallic Wigner crystal phase next to an insulator.

Recent conductance reversal observations are explained by the theory.

Abstract

Nearly a century after Wigner's initial proposal, electron crystals are now a topic of intense experimental and theoretical interest. However, most proposed crystalline phases are commensurate and therefore become insulating in the presence of even weak pinning. In this work we discuss when a commensurate Wigner crystal will spontaneously self dope and develop itinerant carriers, giving rise to an incommensurate and thus metallic Wigner crystal (MWC). We develop a general criterion for the instability of the commensurate crystal which involves the competition between the charge gap at commensurability and a ``packing bias'' whose sign selects whether electron or hole doping is preferred. We then apply these insights to rhombohedral multilayer graphene, where calculations for commensurate crystals reveal instabilities towards self-doping. Carrying out self-consistent Hartree-Fock over the landscape of incommensurate crystals reveals the phase diagram, where a broad MWC phase appears directly adjacent to an insulating Wigner crystal phase. Recent observations of an island of reversed Hall conductance near a putative Wigner crystal phase in rhombohedral graphene are naturally explained by our theory.