Magneto-Seebeck coefficient of the Fermi liquid in three-dimensional Dirac and Weyl semimetals

We investigate dissipationless magneto-Seebeck effect in three-dimensional Dirac and Weyl semimetals. The Hall resistivity ${\rho }_{yx}$ and thermoelectric Hall coefficient ${\alpha }_{xy}$ exhibit plateaus at the quantum limit, where electrons occupy only the zeroth Landau level. In this condition, quantum oscillation in the Seebeck coefficient $S_{xx}\approx {\rho }_{yx}{\alpha }_{xy}$ is suppressed, and the massless fermions are transformed into a Fermi liquid system. We show that the Seebeck coefficient at the quantum limit is expressed by the harmonic sum of Fermi wavelength and thermal de Broglie wavelength scaled by magnetic length.

Figure 1

Log-log plot of ${\rho }_{yx}$ as a function of $B$ at a constant $\mu =7.36\mathrm{meV}$ for several values of $T$. Inset shows the linear plot of ${\rho }_{yx}$ for $B=0-2\mathrm{T}$.

Figure 2

Log-log plot of (a) ${\alpha }_{xy}$ and (b) $S_{xx}$ as a function of $B$ for several values of $T$. The chemical potential is set at $\mu =7.36\mathrm{meV}$. Grey circles indicate the saturated magnetic field, where ${\alpha }_{xy}$ and $S_{xx}$ begin to saturate.

Figure 3

Plot of the scaled Seebeck coefficient $S_{xx}/\mathcal{S}$ as a function of ${\lambda }_H/{\ell }_B$ for constant $\mu =7.36\mathrm{meV}$ for several values of $T$. Inset: $S_{xx}/\mathcal{S}$ at a constant $T=3\mathrm{K}$ for several values of $\mu$.