Seebeck Effect of Dirac Electrons

We investigate the Seebeck effect in a three-dimensional Dirac electron system based on linear response theory and Luttinger’s gravitational potential. The coefficient S is defined by = L12/L11T, where T temperature, L11 L12 are longitudinal coefficients of charge current to electric field temperature gradient, respectively; conductivity thermoelectric conductivity. consider randomly-distributed impurity potentials as source momentum relaxation electrons microscopically calculate rate vertex corrections due impurities. It confirmed that related through Mott’s formula low temperatures when chemical potential lies above gap (|μ| > Δ), irrespective dispersion unconventional energy dependence lifetime electrons. Alternatively, bandgap < functions similar conventional semiconductors; its dependences potential, μ, T, partially captured ∝ (Δ − μ)/kBT for μ 0. takes relatively large value |S| \( \simeq \) 1.7 mV/K at 4.3 K Δ 8 meV assuming doped bismuth.