Pressure induced gap modulation and topological transitions in twisted bilayer and double bilayer graphene

TL;DR

This study investigates how perpendicular pressure affects the electronic and topological properties of twisted bilayer and double bilayer graphene, revealing pressure-induced gap modulation and topological phase transitions.

Contribution

It introduces a method to determine structural deformations under pressure and demonstrates the significant impact of relaxation effects on electronic properties and topological transitions in these materials.

Findings

In-plane relaxation increases with pressure while corrugation height remains constant.

Gaps on electron and hole sides are underestimated without relaxation.

Topological transitions occur in TDBG under pressure with band touching and Chern number transfer.

Abstract

We study the electronic and topological properties of fully relaxed twisted bilayer (TBG) and double bilayer (TDBG) graphene under perpendicular pressure. An approach has been proposed to obtain the equilibrium in-plane structural deformation and out-of-plane corrugation in moir\'{e} superlattices under pressure. We find that the in-plane relaxation becomes much stronger under higher pressure, while the corrugation height in each layer is maintained. The comparison between band structures of relaxed and rigid structures demonstrates that not only the gaps on the electron and hole sides ($\Delta_e$ and $\Delta_h$) are significantly underestimated without relaxation but also the detailed dispersions of the middle bands of rigid structures are rather different from those of relaxed systems. $\Delta_e$ and $\Delta_h$ in TBG reach maximum values around critical pressures with narrowest middle bands. Topological transitions occur in TDBG under pressure with the middle valence and conduction bands in one valley touching and their Chern numbers transferred to each other. The pressure can also tune the gap at the neutrality point of TDBG, which becomes closed for a pressure range and reopened under higher pressure. The behavior of electronic structure of supertlattices under pressure is sensitive to the twist angle $\theta$ with the critical pressures generally increase with $\theta$.