Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene

TL;DR

This paper uses mean-field and RPA calculations to analyze magnetic phases and spin patterns in doped Bernal bilayer graphene with Hubbard interactions, revealing complex magnetic orderings and effects of external fields.

Contribution

It provides a systematic phase diagram of magnetic states in Bernal bilayer graphene at various doping levels and temperatures, including the effects of external displacement fields.

Findings

Identification of Ne9el and stripe magnetic orders.

Resolution of competition between stripe and chiral spin density waves.

External displacement field influences spin pattern configurations.

Abstract

We perform unrestricted Hartree-Fock calculations on the 2D Hubbard model on a honeycomb and bilayer honeycomb lattice at both zero and finite temperatures. Finite size real space calculations are supplemented with RPA calculations in the thermodynamic limit. Our motivation comes from high doping levels achieved in graphene and Bernal bilayer graphene by interacalation. We present phase diagrams in doping and temperature for a moderate Hubbard interaction. The magnetic states we find are classified systematically based on the dominant Fourier components of their spin patterns, their average magnetization and spin incommensurabilities. The dominant spin patterns are N\'eel order and various types of stripes. Around Van Hove filling, we resolve the competition between stripe and chiral spin density waves in the symmetry-broken regime. We also investigate the effect of an applied external displacement field on the spin patterns of BBG.