Strain effect on power factor in monolayer $\mathrm{MoS_2}$

Biaxial strain dependence of electronic structures and thermoelectric properties of monolayer $\mathrm{MoS_2}$, including compressive and tensile strain, are investigated by using local-density approximation (LDA) plus spin-orbit coupling (SOC). Both LDA and LDA+SOC results show that $\mathrm{MoS_2}$ is a direct gap semiconductor with optimized lattice constants. It is found that SOC has important effect on power factor, which can enhance one in n-type doping, but has a obvious detrimental influence for p-type. Both compressive and tensile strain can induce direct-indirect gap transition, which produce remarkable influence on power factor. Calculated results show that strain can induce significantly enhanced power factor in n-type doping by compressive strain and in p-type doping by tensile strain at the critical strain of direct-indirect gap transition. These can be explained by strain-induced accidental degeneracies, which leads to improved Seebeck coefficient. Calculated results show that n-type doping can provide better power factor than p-type doping. These results make us believe that thermoelectric properties of monolayer $\mathrm{MoS_2}$ can be improved in n-type doping by compressive strain.