Ordered states of undoped AB bilayer graphene: bias induced cascade of transitions

TL;DR

This paper uses mean-field theory to map the phase diagram of undoped AB bilayer graphene under an electric field, revealing a cascade of first-order transitions between various insulating states influenced by long-range Coulomb interactions.

Contribution

It introduces a comprehensive mean-field framework that includes long-range Coulomb effects, uncovering multiple bias-induced phase transitions in bilayer graphene.

Findings

Multiple first-order phase transitions occur with varying bias.

Some phases exhibit two inequivalent single-particle gaps.

Transitions involve discontinuous changes in the electronic gap.

Abstract

Using mean-field theory, we determine the electronic phase diagram of undoped AB-stacked bilayer graphene in the presence of a transverse electric field. In addition to multiple competing electronic instabilities characterized by excitonic order parameters, our framework incorporates the long-range Coulomb energy associated with interlayer polarization. This long-range interaction plays a crucial role, as it significantly influences both the structure and the relative energies of the competing ordered states. We derive a set of self-consistency equations and solve them both numerically and analytically. Our findings reveal that, as the bias field is varied, the bilayer undergoes a cascade of first-order transitions between several ordered insulating phases for which order-parameter structures are explicitly identified. Some of these phases are characterized by two inequivalent single-particle gaps, whose magnitudes depend on the valley and spin quantum numbers. Field-driven transitions are accompanied by discontinuous and non-monotonic variations of the single-electron gap. We relate our results to Hartree-Fock numerical calculations and to experimental research, including observations of fractional metallic phases that emerge upon doping the bilayer system.