Strain effects on the spin-orbit-induced band structure splittings in monolayer MoS₂ and graphene

The strain effects on the spin-orbit-induced splitting of the valence-band maximum and conduction-band minimum in monolayer MoS₂ and the gap in graphene are calculated using first-principles calculations. The dependence of these splittings on the various symmetry types of the strain is described by means of an effective Hamiltonian based on the method of invariants, and the parameters in the model are extracted by fitting to the theory. These splittings are related to acoustic-phonon deformation potentials or electron-phonon- coupling matrix elements which enter the spin-dependent scattering theory of conduction in these materials.