Thermoelectric Hall conductivity and figure of merit in Dirac/Weyl materials


We calculate the thermoelectric response coefficients of three-dimensional Dirac or Weyl semimetals as a function of magnetic field, temperature, and Fermi energy. We focus in particular on the thermoelectric Hall coefficient αxy\alpha_{xy} and the Seebeck coefficient SxxS_{xx}, which are well-defined even in the dissipationless limit. We contrast the behaviors of αxy\alpha_{xy} and SxxS_{xx} with those of traditional Schr\"{o}dinger particle systems, such as doped semiconductors. Strikingly, we find that for Dirac materials αxy\alpha_{xy} acquires a constant, quantized value at sufficiently large magnetic field, which is independent of the magnetic field or the Fermi energy, and this leads to unprecedented growth in the thermopower and the thermoelectric figure of merit. We further show that even relatively small fields, such that ωcτ1\omega_c \tau \sim 1 (where ωc\omega_c is the cyclotron frequency and τ\tau is the scattering time), are sufficient to produce a more than 100%100\% increase in the figure of merit.Comment: 10 pages, 5 figure

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