First-principles estimation of the superconducting transition temperature of a metallic hydrogen liquid

Abstract

We present a full density-functional theory-based implementation of the stochastic path-integral approach proposed by Liu et al. [H. Liu, Y. Yuan, D. Liu, X.-Z. Li, and J. Shi, Phys. Rev. Research 2, 013340 (2020)] for estimating the superconducting transition temperature (${T}_{c}$) of a liquid. The implementation is based on the all-electron projector augmented-wave (PAW) method. We generalize Liu et al.'s formalism to accommodate the pseudodescription of electron states in the PAW method. A formula for constructing the overlap operator of the PAW method is proposed to eliminate errors due to the incompleteness of a pseudobasis set. We apply the implementation to estimate ${T}_{c}$'s of metallic hydrogen liquids. It confirms Liu et al.'s prediction that metallic hydrogen could form a superconducting liquid.