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

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 $K,K^{\prime }$ is circumvented by backfolding the $\pi$-bands to the concomitant mini-Brillouin zone of the supercell, reminiscent of their (twisted) moiré 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.

8 pages, 3 figures, Supplementary Material

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• Theory of intervalley-coherent AFM order and topological superconductivity in tWSe${}_2$
• Correlated phases in rhombohedral multilayer graphene
• Pair density wave in quarter metals from a repulsive fermionic interaction in graphene heterostructures: A renormalization group study
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Site-polarized Mott phases competing with a correlated metal in twisted WSe${}_2$
• Charge density waves and stripes in quarter metals of graphene heterostructures