Wigner crystallization in Bernal bilayer graphene

TL;DR

This paper investigates Wigner crystallization in Bernal bilayer graphene, revealing how Berry curvature and trigonal warping influence the formation, properties, and phase boundaries of the WC state under various conditions.

Contribution

It introduces a theoretical model showing Berry curvature induces a spontaneous orbital magnetization in the WC state and explores the effects of trigonal warping on WC phase behavior.

Findings

Berry curvature causes spontaneous orbital magnetization in WC

Trigonal warping leads to doubly re-entrant WC behavior

Phase boundaries depend on density, displacement field, and temperature

Abstract

In Bernal bilayer graphene (BBG), a perpendicular displacement field flattens the bottom of the conduction band and thereby facilitates the formation of strongly-correlated electron states at low electron density. Here, we focus on the Wigner crystal (WC) state, which appears in a certain regime of sufficiently large displacement field, low electron density, and low temperature. We first consider a model of BBG without trigonal warping, and we show theoretically that Berry curvature leads to a new kind of WC state in which the electrons acquire a spontaneous orbital magnetization when the displacement field exceeds a critical value. We then consider the effects of trigonal warping in BBG, and we show that they lead to an unusual ``doubly re-entrant" behavior of the WC phase as a function of density. The rotational symmetry breaking associated with trigonal warping leads to a nontrivial ``minivalley order" in the WC state, which changes abruptly at a critical value of displacement field. In both cases, we estimate the phase boundary of the WC state in terms of density, displacement field, and temperature.