The Seebeck coefficient, $S=L_{12}/\left(T{L}_{11}\right)$, 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 $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$ [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 $S_x<0$ and $S_y>0$ 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 $L_{11}$.

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• First-principles calculations
• Spin-orbit coupling
• Thermoelectric effects
• Dirac semimetal
• Molecular solids
• Two-dimensional electron system
• Tight-binding model