# Interaction-induced insulating states in multilayer graphenes

## TL;DR

This study investigates how electron interactions induce insulating states in multilayer graphene, revealing layer-dependent phase transitions and topologically distinct insulating phases with potential experimental signatures.

## Contribution

It demonstrates the role of electron-electron interactions and band parameters in determining insulating ground states in multilayer graphene, highlighting topological differences.

## Key findings

- Electron interactions open a band gap in multilayer graphene from 2 to 8 layers.
- Distinct topological phases with different Chern numbers are identified.
- Layer-dependent phase stability and topological properties are characterized.

## Abstract

We explore the electronic ground states of Bernal-stacked multilayer graphenes using the Hartree-Fock mean-field approximation and the full-parameter band model. We find that the electron-electron interaction tends to open a band gap in multilayer graphenes from bilayer to 8-layer, while the nature of the insulating ground state sensitively depends on the band parameter $\gamma_2$, which is responsible for the semimetallic nature of graphite. In 4-layer graphene, particularly, the ground state assumes an odd-spatial-parity staggered phase at $\gamma_2 = 0$, while an increasing, finite value of $\gamma_2$ stabilizes a different state with even parity, where the electrons are attracted to the top layer and the bottom layer. The two phases are topologically distinct insulating states with different Chern numbers, and they can be distinguished by spin or valley Hall conductivity measurements. Multilayers with more than five layers also exhibit similar ground states with potential minima at the outermost layers, although the opening of a gap in the spectrum as a whole is generally more difficult than in 4-layer because of a larger number of energy bands overlapping at the Fermi energy.