Interacting electrons on trilayer honeycomb lattices

TL;DR

This paper theoretically investigates the competing electronic instabilities in trilayer honeycomb lattices with ABA and ABC stacking, revealing potential ground states like SDW, charge density wave, and QSH order, influenced by electron interactions.

Contribution

It provides a detailed theoretical analysis of interaction-driven phases in trilayer graphene, highlighting the influence of stacking order and interaction parameters on emergent electronic orders.

Findings

Different instabilities depend on stacking order and interaction strength.

Systems are near the boundary between SDW and QSH regimes.

Interaction-induced gaps are comparable to those in bilayer systems.

Abstract

Few-layer graphene systems come in various stacking orders. Considering tight-binding models for electrons on stacked honeycomb layers, this gives rise to a variety of low-energy band structures near the charge neutrality point. Depending on the stacking order these band structures enhance or reduce the role of electron-electron interactions. Here, we investigate the instabilities of interacting electrons on honeycomb multilayers with a focus on trilayers with ABA and ABC stackings theoretically by means of the functional renormalization group. We find different types of competing instabilities and identify the leading ordering tendencies in the different regions of the phase diagram for a range of local and non-local short-ranged interactions. The dominant instabilities turn out to be toward an antiferromagnetic spin-density wave (SDW), a charge density wave and toward quantum spin Hall (QSH) order. Ab-initio values for the interaction parameters put the systems at the border between SDW and QSH regimes. Furthermore, we discuss the energy scales for the interaction-induced gaps of this model study and put them into context with the scales for single-layer and Bernal-stacked bilayer honeycomb lattices. This yields a comprehensive picture of the possible interaction-induced ground states of few-layer graphene.