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Electronic Thermal Conductivity in Disordered Systems near the Anderson Transition

The energy-energy correlation function has been evaluated for a disordered electron system in the absence of the electron-electron interaction. Consistently with a generalized Ward identity associated with the continuity equation for energy transport, particle and energy diffusion are shown to be governed by the same diffusion coefficient. This result confirms the general validity of the Wiedemann and Franz law in the presence of elastic scattering. In particular, it is predicted that whenever the electron-electron interaction can be neglected, electrical and thermal conductivities scale to zero in the same way near the localization transition.