Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene

TL;DR

This paper develops a minimal low-energy model for Bernal bilayer graphene using supercell Wannier functions, capturing spectral and Berry curvature features, and revealing weak electron-electron interactions at low densities.

Contribution

It introduces a real-space supercell Wannier basis for Bernal bilayer graphene, bridging ab-initio and continuum models, and elucidates the low-energy physics with a symmetric lattice approach.

Findings

Supercell Wannier functions accurately reproduce spectral weight and Berry curvature.

Low-energy physics is dominated by weak electron-electron interactions.

Provides a unified lattice description connecting ab-initio and continuum theories.

Abstract

We derive a minimal low-energy model for Bernal bilayer graphene and related rhombohedral graphene multilayers at low electronic densities by constructing Wannier orbitals defined in real-space supercells of the original primitive cell. Starting from an ab-initio electronic structure theory comprising the atomic carbon $p_z$-orbitals, momentum locality of the Fermi surface pockets around $K,K'$ is circumvented by backfolding the $\pi$-bands to the concomitant mini-Brillouin zone of the supercell, reminiscent of their (twisted) moir\'e counterparts. The supercell Wannier functions reproduce the spectral weight and Berry curvature of the microscopic model and offer an intuitive real-space picture of the emergent physics at low electronic densities being shaped by flavor-polarized wave packets with mesoscopic extent. By projecting an orbital-resolved, dual-gated Coulomb interaction to the effective Wannier basis, we find that the low-energy physics of Bernal bilayer graphene is governed by weak electron-electron interactions. Our study bridges between existing continuum theories and ab-initio studies of small Fermi pocket systems like rhombohedral graphene stacks by providing a symmetric lattice description of their low-energy physics.