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

Abstract

We have calculated the thermoelectric conductivity tensor εij and the thermal conductivity tensor λij 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 electrical conductivity tensor σij 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 εij (λij). We further present plots of the commensurability oscillations δεij, δλij, δκij, and δSij in εij, λij, (an alternative, more standard definition of) the thermal conductivity tensor κij, and the thermopower tensor Sij, calculated using typical parameters for a ULSL fabricated from a GaAs/AlGaAs two-dimensional electron gas (2DEG). Notable features of the δSij are (i) anisotropic behavior (δSxx ≠ δSyy) and (ii) the dominance of the xy component over the other components (\(|\delta S_{xy}| \gg |\delta S_{yx}|,|\delta S_{xx}|,|\delta S_{yy}|\)). The latter clearly indicates that the two Nernst coefficients, Sxy and Syx, 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 δSij thus far.