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

We study the electronic and topological properties of fully relaxed twisted bilayer (TBG) and twisted 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 moire 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. A comparison between the 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 the 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 the electronic structure of superlattices under pressure is sensitive to the twist angle. with the critical pressures generally increasing with