First-principles study on heat and charge transport of warm dense aluminum with Kohn-Sham and stochastic density functional theory*

Traditional Kohn-Sham density functional theory (KSDFT) is one of the most popular quantum-mechanics-based methods in modeling materials since it balances the accuracy and efficiency well. Accurately predicting electron transport coefficients is crucial for understanding warm dense matter. The Kubo-Greenwood formula, within the framework of KSDFT, is commonly employed to evaluate the electrical and thermal conductivities of electrons. However, in some works, the velocity operator of this formula is approximated by the momentum operator without non-local potential corrections. Moreover, traditional KSDFT, based on the diagonalization method, is inefficient for simulating high-temperature systems. Recently, stochastic density functional theory [Phys. Rev. Lett. 111, 106402 (2013)] (SDFT) and its improved theory, mixed stochastic-deterministic density functional theory [Phys. Rev. Lett. 125, 055002 (2020)] (MDFT) are developed based on stochastic orbitals. These methods enable more efficient simulation of high-temperature systems. In this study, we carefully examine this approximation of the velocity operator in warm dense aluminum at temperatures ranging from 0.1 eV to 10 eV and at densities of 2.35 g/cm³ and 2.7 g/cm³, using both pseudopotential with 3 valence electrons and 11 valence electrons. Our findings indicate that considering the non-local potential effect is essential for accurately calculating the heat and charge transport properties of electrons. Furthermore, we observe that the frozen-core approximation is invalid for calculating conductivities before the ionization of corresponding core electrons occurs. Additionally, we develop a new Kubo-Greenwood formula within the framework of MDFT to calculate thermal and electrical conductivities. This work demonstrates that the proposed method is capable of accurately calculating electronic thermal and electrical conductivities at temperatures of hundreds of eV.