Abstract
We develop a nonperturbative approach for calculating the superconducting transition temperatures (Tc'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 Tc, the linearized Eliashberg equations are reestablished nonperturbatively. We apply the approach to estimate Tc's of metallic hydrogen liquids. It indicates that metallic hydrogen liquids in the pressure regime from 0.5 to 1.5TPa have Tc's well above their melting temperatures and therefore are superconducting liquids.1 MoreReceived 29 January 2019Revised 28 January 2020Accepted 30 January 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.013340Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectron-phonon couplingMethods in superconductivityPressure effectsSuperconducting phase transitionTransition temperaturePhysical SystemsHigh-temperature superconductorsLiquidsUnconventional superconductorsTechniquesDensity functional theoryEliashberg theoryGreen's function methodsCondensed Matter, Materials & Applied Physics
Highlights
Mercury, the only metallic element which is a liquid under the ambient conditions, happens to be the first superconductor ever discovered
We find that metallic hydrogen liquids in the pressure regime from 0.5 to 1.5 TPa have Tc’s well above their melting temperatures and are superconducting liquids
The Coulomb interaction introduces a number of revisions to our result and derivation: (i) when determining the Green’s function G[R(τ )], one needs to introduce a self-energy functional c[G] which accounts for the effect of the Coulomb interaction [25]
Summary
The only metallic element which is a liquid under the ambient conditions, happens to be the first superconductor ever discovered. It is predicted that hydrogen forms an atomic metal [2] and has a relatively low melting temperature in the pressure regime from 0.5 to 1.5 TPa [3,4]. Tc predicted for the solid phase of metallic hydrogen is much higher than the melting temperature [5]. It raises an intriguing question: Can a metallic hydrogen liquid be superconducting?. The density range is believed not in the regime forming the atomic metal [2] Their formalism is based on a heuristic generalization of the conventional electron-phonon coupling (EPC) theory [7,8], which is developed for.
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