Impurity Effect in the Quantum Nernst Effect

We theoretically study the Nernst effect and the Seebeck effect in a two-dimensional electron gas in a strong magnetic field and a temperature gradient under adiabatic condition. We recently predicted for a pure system in the quantum Hall regime that the Nernst coefficient is strongly suppressed and the thermal conductance is quantized due to quantum ballistic transport. Taking account of impurities, we here compute the Nernst coefficient and the Seebeck coefficient when the chemical potential coincides with a Landau level. We adopt the self-consistent Born approximation and consider the linear transport equations of the thermal electric transport induced by the temperature gradient. The thermal conductance and the Nernst coefficient are slightly modified from the pure case and the Seebeck coefficient newly appears because of the impurity scattering of electrons in the bulk states.