Superconductivity of Liquids*

We develop a non-perturbative approach for calculating the superconducting transition temperatures (T_c's) of liquids. The electron-electron scattering amplitude induced by electron-phonon coupling (EPC), from which an effective pairing interaction can be inferred, is related to the fluctuation of the T-matrix of electron scattering induced by ions. By applying the relation, EPC parameters can be extracted from a path-integral molecular dynamics simulation. For determining T_c, the linearized Eliashberg equations are re-established non-perturbatively. We apply the approach to estimate T_c's of metallic hydrogen liquids. It indicates that metallic hydrogen liquids in the pressure regime from 0.5 to 1.5 TPa have T_c's well above their melting temperatures, therefore are superconducting liquids.
[1] H. Liu, Y. Yuan, D. Liu, X.-Z. Li, and J. Shi, ArXiv:1901.02114 (2019).