Twistronics versus straintronics in twisted bilayers of graphene and transition metal dichalcogenides

TL;DR

This paper develops an analytical framework to understand how strain affects the electronic flat bands in twisted bilayers of graphene and TMDs, providing insights into tuning their electronic properties near the magic angle.

Contribution

It derives the low-energy Hamiltonian for strained twisted bilayers of graphene and TMDs, offering analytical expressions for strain effects on Dirac velocities and flat band emergence.

Findings

Strain modifies Dirac velocities and flat band conditions.

Strain can adjust twist angles towards the magic angle.

Analytical results align with numerical and experimental data.

Abstract

Several numerical studies have shown that the electronic properties of twisted bilayers of graphene (TBLG) and transition metal dichalcogenides (TMDs) are tunable by strain engineering of the stacking layers. In particular, the flatness of the low-energy moir\'e bands of the rigid and the relaxed TBLG was found to be, substantially, sensitive to the strain. However, to the best of our knowledge, there are no full analytical calculations of the effect of strain on such bands. We derive, based on the continuum model of moir\'e flat bands, the low-energy Hamiltonian of twisted homobilayers of graphene and TMDs under strain at small twist angles. We obtain the analytical expressions of the strain-renormalized Dirac velocities and explain the role of strain in the emergence of the flat bands. We discuss how strain could correct the twist angles and bring them closer to the magic angle $\theta_m\sim1.05^{\circ}$ of TBLG and how it may reduce the widths of the lowest-energy bands at charge neutrality of the twisted homobilayer of TMDs. The analytical results are compared with numerical and experimental findings and also with our numerical calculations based on the continuum model.