Modified tight-binding model for strain effects in monolayer transition metal dichalcogenides

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) have emerged as a materials paradigm for realizing next-generation on-chip electronic and optoelectronic devices. Strain engineering is actively pursued to tune the electronic properties of 2D TMDCs. However, a generalizable, analytical approach for describing the underlying physics of strain effects on band structure is still lacking. Here, we develop a tight-binding model (TBM) that incorporates strain effect to characterize the band structure tuning of TMDC $({\mathrm{MoS}}_{2},$ ${\mathrm{MoSe}}_{2},$ ${\mathrm{WS}}_{2}, \text{and} {\mathrm{WSe}}_{2})$ monolayers under biaxial strain fields; strain-dependent Slater-Koster parameters are employed to describe electron hopping and orbital overlap in the strained monolayers. Our approach follows from the Wills-Harrison suggestions of a linear relationship between biaxial strain and Slater-Koster parameters. This leads to a linear dependence of the electronic band gap on applied strain for both direct-indirect $({\mathrm{MoX}}_{2})$ and indirect-direct $({\mathrm{WX}}_{2})$ band gap transitions. We further study the influence of biaxial strain on the energy differences between different high-symmetry points in $k$ space to deduce the physical origin of strain-induced variations in the band gap type and size. In this process, we select different TBMs (6- or 11-band) and compare them with different first-principles calculation results (DFT-PBE or DFT-HSE) to demonstrate the effectiveness and completeness of our method. Building on this model, we also examined the changes in effective mass and optical conductivity of TMDCs under strain, offering insights that can aid in the development of practical device applications utilizing these materials. Our investigation may be extended to general strained monolayer TMDCs, paving the way for exploring the electronic properties of nanotubes, wrinkled 2D materials, and van der Waals heterostructures under inhomogeneous strain.