Theory of Strain in Monolayer Transition Metal Dichalcogenides: Electronic Structure and Spin/Orbital Hall Effects in MoS₂

Strain has emerged as an important tool to control the electronic properties of two-dimensional monolayer materials such as graphene and the transition-metal dichalcogenides (TMD). One of the interesting aspects of the TMDs such as the MoS₂ is the presence of orbital moments at the valley points of the Brillouin zone, which leads to many interesting phenomena such as the orbital Hall effect. Here we present a systematic theory of the strain modification of the electronic structure and the orbital and spin Hall effects under general strain condition in the TMDs. We adopt an approach for the electronic structure different from the earlier works, which leads to a simpler model Hamiltonian for the valley points under strain condition. The strain Hamiltonian is validated by comparing with the results of the density functional theory (DFT). Furthermore, using DFT calculations, the hamiltonian parameters as well as the spin and orbital Hall conductivities (SHC/OHC) are computed for MoS₂, which is a typical member of the semiconducting TMDs. The OHC remains strong even under the strain condition, while the SHC continues to remain relatively small, making the TMDs excellent candidate materials for the observation of the OHE, both with or without strain