Systematic study of the Wiedemann-Franz law in the quantum-Hall-effect regime

A systematic study of the Wiedemann-Franz law in the quantum-Wall-effect re gime is presented. For this purpose the diffusion thermal conductivity tens or is calculated for a two-dimensional electron gas at low temperatures in a quantizing magnetic field. The range of validity of the Wiedemann-Franz l aw is investigated performing both analytical and numerical calculations. T he analysis shows that for the diagonal component of the thermal conductivi ty, the Wiedemann-Franz law is violated with decreasing Landau level broade ning. Responsible is the coefficient N-xx and specifically the effect of th e energy derivatives of the diagonal electrical conductivity and consequent ly the shape of the density of states. For the nondiagonal components we ob tain smaller deviations. We give physical interpretations for the resulted behavior. [S0163-1829(99)05408-9].