Seebeck and Nernst effects of pseudospin-1 fermions in the α - T3 model under magnetic fields

We numerically study the Seebeck and Nernst effects of pseudospin-1 fermions in the alpha - T-3 model under magnetic fields by combining the nonequilibrium Green's function and the Landauer-B & uuml;ttiker formalism with the Str & eacute;da formula. In the alpha = 0 limit under strong magnetic fields, our results are in good agreement with theoretical results of graphene. Distinguishing from the case of alpha = 0, we find three characteristic features and discuss them in detail analytically for alpha > 0: (i) The inverse of the peak height of the Seebeck coefficient is -e/ln 2k(B) [n(p) + sign(n(p))delta], with delta = 1/2 for alpha > 0 while delta = 0 for alpha = 0, where n(p) denotes the n(p)th peak near -e the Dirac point. We show that delta is determined by the Hall plateau series. (ii) The highest peak of the Seebeck coefficient is much higher than other peaks. This highest peak is ascribed to the vanishing of the Hall conductivity due to the energy gap between the flat band and lowest Landau level. (iii) There exists a negative peak near the Dirac point. We relate this unique behavior to the vanishing of the Hall conductivity near the Dirac point and the isolated flat band. Meanwhile, the peak of the Nernst coefficient for alpha = 0 splits into double peaks by increasing alpha and the height is enhanced. Additionally, the effects of temperatures, disorders, the strength of magnetic field, and edge patterns are also investigated. These findings provide theoretical foundation for future experimental studies on the thermoelectric properties based on the alpha - T-3 materials.