An empirical law on the finite-size effects in electronic transport calculations of tungsten

When the size of a supercell employed in theoretical calculations is smaller obviously than the mean free path of electrons in metals, the computed values of the electrical conductivity and the electronic thermal conductivity show a striking finite-size effect, and such a size-dependent value cannot be used for direct comparison with that from experiments. We hereby propose an empirical law to unified describe the relation between the conductivity (including the electrical conductivity and the electronic thermal conductivity) of infinite-size crystal and that of finite-size supercell in calculations for tungsten (W). Our calculations demonstrate that it is very convenient to achieve the electrical conductivity and the electronic thermal conductivity of W metal by using this empirical law. In addition, we provide a simple power law (∼T−1.35) to describe the finite-size effects at different temperatures. Furthermore, the mean free path of electrons, which tightly correlates to the finite-size effects exhibited in the electronic transport calculations of W at different temperatures, are revealed. The proposed empirical law in this work is robust and may be valid for other metals.