  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.
