Effect of small-angle scattering on the anisotropic behavior of the commensurability oscillations in the thermoelectric power and the thermal conductivity of unidirectional lateral superlattices

We have calculated the thermoelectric conductivity tensor $\varepsilon_{ij}$ 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), based on the asymptotic analytic formulas of the 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 $\varepsilon_{ij}$ ($\lambda_{ij}$). We further present plots of the commensurability oscillations $\delta\varepsilon_{ij}$, $\delta\lambda_{ij}$, and $\delta S_{ij}$ in $\varepsilon_{ij}$, $\lambda_{ij}$, 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 ($\delta S_{xx} \ne \delta S_{yy}$) and (ii) the dominance of the $xy$ component over the other components ($|\delta S_{xy}| \gg |\delta S_{yx}|, |\delta S_{xx}|, |\delta S_{yy}|$). 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.