Atomistic substrate relaxation effects in the band gaps of graphene on hexagonal boron nitride

TL;DR

This study investigates how atomistic substrate relaxation influences the electronic band gaps in graphene on hexagonal boron nitride across various twist angles, revealing significant effects on gap size and behavior.

Contribution

It provides a detailed analysis of substrate relaxation effects on band gaps in G/h-BN, highlighting the importance of relaxation schemes in accurately modeling electronic properties.

Findings

Primary gap decreases with substrate rigidity.

Maximum primary gap near 0.6° twist angle.

Secondary gap drops to zero beyond 1° twist.

Abstract

We assess the impact of atomistic substrate lattice relaxation schemes in the primary band gap at charge neutrality and the secondary valence band gap of graphene on hexagonal boron nitride (G/h-BN) as a function of twist angle. For zero twist angle, the primary gap decreases from $\sim 30$~meV in fully relaxed suspended G/h-BN bilayers, to $\sim 9$~meV when the remote h-BN substrate layer is kept rigid, and down to $\sim 3$~meV in completely rigid structures. In the presence of relaxations, the primary gap shows a maximum near $\sim 0.6^{\circ}$ coinciding with energetic stabilization due to alignment between the moir\'e pattern and the graphene lattice vectors, while the secondary valence band gap drops from $\sim 12$~meV down to zero beyond twist angles of $\sim 1^{\circ}$. A small but finite primary gap on the order of $\sim 1$~meV, with a mass sign favoring electronic occupation of carbon atop boron, persists across twist angles from $0^{\circ}$ to $30^{\circ}$ for all sliding configurations, and switches sign for twist angles between $30^{\circ}$ and $60^{\circ}$.