J. Phys. Soc. Jpn. 91, 054603 (2022) [10 Pages]
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Seebeck Effect of Dirac Electrons

Junji Fujimoto1, , and Masao Ogata1,2
+ Affiliations
1Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan2Trans-scale Quantum Science Institute, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
Received November 9, 2021; Accepted March 23, 2022; Published April 22, 2022

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

©2022 The Physical Society of Japan
https://doi.org/10.7566/JPSJ.91.054603

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