Transition to metallization in warm dense helium-hydrogen mixtures using stochastic density functional theory

The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense matter. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes computationally expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature.

In this talk, I will review our recent developments to calculate the KS conductivity within the stochastic DFT framework, which requires knowledge only of the KS Hamiltonian but not its eigenstates and values. The method allows for an accurate description of the entire spectrum, including the high-frequency range, unlike the deterministic method which is compelled to introduce a high-frequency cutoff due to memory and computational time constraints. The computational effort associated with the method scales linearly with system size and reduces in proportion to the temperature, unlike the cubic increase with traditional deterministic approaches.

We applied the method to helium-hydrogen mixtures in the warm dense matter regime at temperatures of ∼60,000 K and find that the system displays two conductivity phases, where a transition from nonmetal to metal occurs when hydrogen atoms constitute ∼0.3 of the total atoms in the system.