Thermomagnetic Effect in the Quantum Hall System

We calculate the Seebeck Sxx and Nernst Syx components of the thermopower tensor Ŝ in the quantum Hall system, using analytical formulas of the conductivity tensor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\sigma}$$\end{document} that we deduced in a previous publication. The results basically reproduce the magnetic field dependence of experimentally observed behavior of Sxx and Syx. With the aid of the Mott relation valid at low temperatures, we can further simplify the expressions and obtain analytical formulas for Sxx and Syx. The Mott relation predicts that both Sxx and Syx grow linearly with temperature T. To examine the range of validity of the formula based on the Mott relation, we investigate the temperature dependence of the height of the |Sxx| peak at the first excited (N = 1) Landau level for various values of the impurity scattering time τq. The results calculated with the more general integral formulas are seen to deviate from the linear T dependence and asymptotically approach the universal value (2ln 2/3)(kB/e) above \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T \simeq \hbar / (2 \tau_{\rm q} k_{\rm B}).$$\end{document}