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 $\varepsilon_{ij}$ and the thermal conductivity tensor $λ_{ij}$ 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 $σ_{ij}$ 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 $\varepsilon_{ij}$ ($λ_{ij}$). We further present plots of the commensurability oscillations $δ\varepsilon_{ij}$, $δλ_{ij}$, $δκ_{ij}$, and $δS_{ij}$ in $\varepsilon_{ij}$, $λ_{ij}$, (an alternative, more standard definition of) the thermal conductivity tensor $κ_{ij}$, 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 $δS_{ij}$ are (i) anisotropic behavior ($δS_{xx} \ne δS_{yy}$) and (ii) the dominance of the $xy$ component over the other components ($|δS_{xy}| \gg |δS_{yx}|, |δS_{xx}|, |δS_{yy}|$). 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 $δS_{ij}$ thus far.