Spin-orbit coupling effect on the Seebeck coefficient in Dirac electron systems in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mtext>−</mml:mtext> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mtext>BE

The Seebeck coefficient, $S={L}_{12}/(T{L}_{11})$, which is proportional to a ratio of the thermoelectric conductivity ${L}_{12}$ to the electric conductivity ${L}_{11}$, with $T$ being temperature, is examined for two-dimensional Dirac electrons in the three-quarter-filled organic conductor $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{I}}_{3}$ [BETS = BEDT-TSeF = bis(ethylenedithio)tetraselenafulvalene] at ambient pressure. Using a tight-binding model obtained with the first-principles relativistic density functional theory method [Tsumuraya and Suzumura, Eur. Phys. J. B 94, 17 (2021)], we calculate $S$ in the presence of the impurity and electron-phonon scatterings. We show that ${S}_{x}&lt;0$ and ${S}_{y}&gt;0$ at high temperatures, where ${S}_{x}$ (${S}_{y}$) denotes $S$ perpendicular (parallel) to the molecular stacking axis. There is a sign change of ${S}_{y}$ with increasing $T$. We find that at low temperatures the absolute value of $S$ is enhanced by the spin-orbit coupling. The Seebeck coefficient is examined by dividing it into components of the conduction and valence bands; we find that the electron and hole contributions compete with each other. Such $T$ dependence of $S$ is clarified using the spectral conductivity, which determines ${L}_{12}$ and ${L}_{11}$.