Broken symmetry states in bilayer graphene in electric and in-plane magnetic fields

TL;DR

This paper investigates the broken symmetry states in bilayer graphene under electric and magnetic fields, emphasizing the importance of momentum-dependent gaps and mapping the phase diagram with experimental relevance.

Contribution

It provides a detailed numerical analysis of gap equations considering momentum dependence and derives a phase diagram showing the stability of different phases in bilayer graphene.

Findings

Momentum dependence reduces gap magnitudes by an order of magnitude.

The layer antiferromagnetic state remains stable at large in-plane magnetic fields.

The quantum valley Hall phase becomes dominant at high perpendicular electric fields.

Abstract

Broken symmetry states in bilayer graphene in perpendicular electric $E_\perp$ and in-plane magnetic $B_\parallel$ fields are studied in the presence of the dynamically screened long-range Coulomb interaction and the symmetry-breaking contact four-fermion interactions. The integral gap equations are solved numerically, and it is shown that the momentum dependence of gaps is essential: It diminishes by an order of magnitude the gaps compared to the case of momentum-independent approximation, and the obtained gap magnitudes are found to agree well with existing experimental values. We derived a phase diagram of bilayer graphene at the neutrality point in the plane $(B_\parallel,E_\perp)$ showing that the (canted) layer antiferromagnetic (LAF) state remains a stable ground state of the system at large $B_\parallel$. On the other hand, while the LAF phase is realized at small values of $E_{\perp}$, the quantum valley Hall (QVH) phase is the ground state of the system at values $E_{\perp}>E_{cr}(B_\parallel)$, where a critical value $E_{cr}(B_\parallel)$ increases with in-plane magnetic field $B_{||}$.