  Effect of spin-orbit coupling (SOC) on Dirac electrons in the organic
conductor $\alpha$-(BETS)$_2$I$_3$ [BETS =
bis(ethylenedithio)tetraselenafulvalene] has been examined by calculating
electric conductivity and spin magnetic susceptibility. A tight-binding (TB)
model with real and imaginary transfer energies is derived using
first-principles density-functional theory method. The conductivity without the
SOC depends on both anisotropies of the velocity of the Dirac cone and the
tiling of the cone. Such conductivity is suppressed by the SOC, which gives
rise to the imaginary part of the transfer energy. Due to the SOC, we find at
low temperatures that the reduction of the conductivity becomes large and that
the anisotropy of the conductivity is reduced. A nearly constant conductivity
at high temperatures is obtained by an electron--phonon (e--p) scattering.
Further, the property of the Dirac cone is examined for the spin
susceptibility, which is mainly determined by the density of states (DOS). The
result is compared with the case of the organic conductor
$\alpha$-(BEDT-TTF)$_2$I$_3$ [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene],
which provides the Dirac cone without the SOC. The relevance to experiments is
discussed.
