Electronic thermal conductivity at high temperatures: Violation of the Wiedemann-Franz law in narrow-band metals

We study the electronic part of the thermal conductivity of metals. We present two methods for calculating , a quantum Monte-Carlo method and a method where the phonons but not the electrons are treated semiclassically (SC). We compare the two methods for a model of alkali-doped C₆₀, A₃C₆₀, and show that they agree well. We then mainly use the SC method, which is simpler and easier to interpret. We perform SC calculations for Nb for large temperatures T and find that increases with T as (T)=a+bT, where a and b are constants, consistent with a saturation of the mean free path, l, and in good agreement with experiment. In contrast, we find that for A₃C₆₀, (T) decreases with T for very large T. We discuss qualitatively the reason for this in the limit of large T. We give a quantum-mechanical explanation of the saturation of l for Nb and derive the Wiedemann-Franz law in the limit of TW, where W is the bandwidth. In contrast, due to the small W of A₃C₆₀, the assumption TW can be violated. We show that this leads to (T)~T^−3/2 for very large T and a strong violation of the Wiedemann-Franz law.

©2006 The American Physical Society