Electrical Conductivity of Iron under Earth-Core Conditions from Time-Dependent Density Functional Theory

Time-dependent density functional theory (TDDFT) enables calculating electronic transport properties in the warm dense matter (WDM) and is an alternative to present state-of-the-art approaches. In the real-time formalism of TDDFT (RT-TDDFT), the electrical conductivity is directly computed from the time evolution of the electronic current density and provides direct means to assess the validity of Ohm's law in WDM. Without relying on the methods of diagonalization, the method is computationally fast compared to linear-response TDDFT (LR-TDDFT). We present TDDFT calculations of the electrical conductivity in iron within the pressure and temperature ranges found in Earth's core and discuss the ramifications of using TDDFT for calculating the electrical conductivity in contrast to the Kubo-Greenwood (KG) formalism and dielectric models.