Motivated by recent studies on topologically nontrivial moiré bands in twisted bilayer transition metal dichalcogenides (TMDs), we study ${\mathrm{MoTe}}_2$ bilayer systems subject to pressure, which is applied perpendicular to the material surface. We start our investigation by first considering an untwisted bilayer systems with an arbitrary relative shift between layers; a symmetry analysis for this case permits us to obtain a simplified effective low-energy Hamiltonian valid near the important $\mathbf{K}$ valley region of the Brillouin zone. Ab initio density functional theory (DFT) was then employed to obtain relaxed geometric structures for pressures within the range of 0.0–3.5 GPa and corresponding band structures. The DFT data were then fitted to the low-energy Hamiltonian to obtain a pressure-dependent Hamiltonian. We then applied our model to a twisted system by treating the twist as a position-dependent shift between layers—here, we assume rigid layers, which is a crucial simplification. In summary, this approach allowed us to obtain the explicit analytical expressions for a Hamiltonian that describes a twisted ${\mathrm{MoTe}}_2$ bilayer under pressure. Our Hamiltonian then permitted us to study the impact of pressure on the band topology of the twisted system. As a result, we identified many pressure-induced topological phase transitions as indicated by changes in valley Chern numbers. Moreover, we found that pressure could be employed to flatten bands in some of the cases we considered.

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• Electronic structure
• Topological phase transition
• Transition metal dichalcogenides
• Twisted heterostructures
• Two-dimensional electron system
• Density functional theory