Anisotropic Behavior of the Thermoelectric Power and the Thermal Conductivity in a Unidirectional Lateral Superlattice: A Typical Anisotropic System Exhibiting Two Distinct Nernst Coefficients

We have calculated the thermoelectric conductivity tensor ${\epsilon }_{ij}$ and the thermal conductivity tensor ${\lambda }_{ij}$ of a unidirectional lateral superlattice (ULSL) ($i,j=x,y$, with the $x$-axis aligned to the principal axis of the ULSL), %, given as the first- and the second-order moments, employing based on the asymptotic analytic formulas of the electrical conductivity tensor ${\sigma }_{ij}$ in the literature valid at low magnetic fields where large numbers of Landau levels are occupied. With the resulting analytic expressions, we clarify the conditions for the Mott formula (Wiedemann-Franz law) to be applicable with high precision to ${\epsilon }_{ij}$ (${\lambda }_{ij}$). We further present plots of the commensurability oscillations $\delta {\epsilon }_{ij}$, $\delta {\lambda }_{ij}$, $\delta {\kappa }_{ij}$, and $\delta S_{ij}$ in ${\epsilon }_{ij}$, ${\lambda }_{ij}$, (an alternative, more standard definition of) the thermal conductivity tensor ${\kappa }_{ij}$, and the thermopower tensor $S_{ij}$, calculated using typical parameters for a ULSL fabricated from a GaAs/AlGaAs two-dimensional electron gas (2DEG). Notable features of the $\delta S_{ij}$ are (i) anisotropic behavior ($\delta S_{xx}\mathrm{\ne }\delta S_{yy}$) and (ii) the dominance of the $xy$ component over the other components ($\mathrm{\mid }\delta S_{xy}\mathrm{\mid }\gg \mathrm{\mid }\delta S_{yx}\mathrm{\mid },\mathrm{\mid }\delta S_{xx}\mathrm{\mid },\mathrm{\mid }\delta S_{yy}\mathrm{\mid }$). The latter clearly indicates that the two Nernst coefficients, $S_{xy}$ and $S_{yx}$, can be totally different from each other in an anisotropic system. Both (i) and (ii) are at variance with the previous theory and are attributable to the inclusion of a damping factor due to the small-angle scattering characteristic of GaAs/AlGaAs 2DEGs, which have not been taken into consideration in $\delta S_{ij}$ thus far.