Theory of strain-dependent electronic structure and the valley orbital model for the monolayer transition metal dichalcogenides MX₂

The broken inversion symmetry in transition metal dichalcogenides (TMDs) such as MoS₂ leads to coupled spin-valley physics, which is well described by the low-energy valley-orbital model applicable to the electronic structure near the K/K' valley points. The spin-valley physics can be modified by introducing strain into the system, which has emerged as an important tool to manipulate the electronic properties. Here, we develop a valley-orbital model for the general strain condition by adopting an approach different from earlier works, which allows us to formulate the model valid around the valley points. The form of the strain Hamiltonian, which we obtain to linear order in momentum q about the valley points, is developed by considering a tight-binding model under strain condition and validated by comparing with the density-functional theory (DFT) results. The Hamiltonian properly describes the shape change of the energy contours and the shift of the valley extrema points under a general strain condition. The total energy expression follows the appropriate form for the D_3h symmetry, which is well known from the theory of elasticity. The Hamiltonian parameters are presented for a number of TMDs obtained from the DFT calculations. Our results are valuable for describing strain-dependent valley-orbital physics for this important class of materials.