Quantum Nernst Effect in a Bismuth Single Crystal

We calculate the phonon-drag contribution to the transverse (Nernst) thermoelectric power $S_{yx}$ in a bismuth single crystal subjected to a quantizing magnetic field. The calculated heights of the Nernst peaks originating from the hole Landau levels and their temperature dependence reproduce the right order of magnitude for those of the pronounced magneto-oscillations recently reported by Behnia et al [Phys.Rev.Lett. 98, 166602 (2007)]. A striking experimental finding that $S_{yx}$ is much larger than the longitudinal (Seebeck) thermoelectric power $S_{xx}$ can be naturally explained as the effect of the phonon drag, combined with the well-known relation between the longitudinal and the Hall resistivity $rho_{xx}>>|rho_{yx}|$ in a semi-metal bismuth. The calculation that includes the contribution of both holes and electrons suggests that some of the hitherto unexplained minor peaks located roughly at the fractional filling of the hole Landau levels are attributable to the electron Landau levels.