Flat band electrons and interactions in rhombohedral trilayer graphene

TL;DR

This paper investigates the electronic properties of flat bands in rhombohedral trilayer graphene, emphasizing the role of electron interactions and proposing an effective lattice model to explore potential magnetic ordering.

Contribution

It introduces a comprehensive interaction-only lattice model for flat band electrons in trilayer graphene, including long-range Coulomb interactions and flat band projection techniques.

Findings

Interaction favors ferromagnetic quantum crystal formation under certain conditions

Full Coulomb interaction terms are incorporated into the model

Flat band electrons are described using surface-localized ansatz states

Abstract

Multilayer graphene systems with a rhombohedral stacking order harbor nearly flat bands in their single-particle spectrum. We propose ansatz states to describe the surface-localized states of flat band electrons. The absence of kinetic dispersion near the fermi level leaves the interaction as a dominate mechanism to govern the low energy physics of a low density electron system. We build up an effective lattice model in two interacting low-energy bands, where the full terms of the Coulomb interaction, including those long-range and off-diagonal parts, have been considered. The interaction matrix coefficients in the many-body Hamiltonian model are directly calculated for a trilayer system using orthonormal Wannier basis. We then present a flat-band projection to yield an interaction-only lattice model for flat band electrons. We find that this limited model might energetically favor a ferromagnetic quantum crystal under certain conditions.