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 alpha(xy) and the Seebeck coefficient S-xx which are well-defined even in the dissipationless limit. We contrast the behaviors of alpha(xy) and S-xx with those of traditional Schrodinger particle systems, such as doped semiconductors. Strikingly, we find that for Dirac materials 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 omega(c)tau similar to 1(where omega(c) is the cyclotron frequency and t is the scattering time), are sufficient to produce a more than 100% increase in the figure of merit.