  Pressure dependence of electronic structures and thermoelectric properties of
$\mathrm{Mg_2Sn}$ are investigated by using a modified Becke and Johnson (mBJ)
exchange potential, including spin-orbit coupling (SOC). The corresponding
value of spin-orbit splitting at $\Gamma$ point is 0.47 eV, which is in good
agreement with the experimental value 0.48 eV. With the pressure increasing,
the energy band gap first increases, and then decreases. In certain doping
range, the power factor for n-type has the same trend with energy band gap,
when the pressure increases. Calculated results show that the pressure can lead
to significantly enhanced power factor in n-type doping below the critical
pressure, and the corresponding lattice thermal conductivity near the critical
pressure shows the relatively small value. These results make us believe that
thermoelectric properties of $\mathrm{Mg_2Sn}$ can be improved in n-type doping
by pressure.
