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Effect of spin-orbit coupling (SOC) on Dirac electrons in the organicconductor $\alpha$-(BETS)$_2$I$_3$ [BETS =bis(ethylenedithio)tetraselenafulvalene] has been examined by calculatingelectric conductivity and spin magnetic susceptibility. A tight-binding (TB)model with real and imaginary transfer energies is derived usingfirst-principles density-functional theory method. The conductivity without theSOC depends on both anisotropies of the velocity of the Dirac cone and thetiling of the cone. Such conductivity is suppressed by the SOC, which givesrise to the imaginary part of the transfer energy. Due to the SOC, we find atlow temperatures that the reduction of the conductivity becomes large and thatthe anisotropy of the conductivity is reduced. A nearly constant conductivityat high temperatures is obtained by an electron--phonon (e--p) scattering.Further, the property of the Dirac cone is examined for the spinsusceptibility, which is mainly determined by the density of states (DOS). Theresult 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 isdiscussed.

Electric and Magnetic Responses of Two-dimensional Dirac Electrons in Organic Conductor $\alpha$-(BETS)$_2$I$_3$