High-T _c superconductivity in H₃S: pressure effects on the superconducting critical temperature and Cooper pair distribution function

Abstract

We use first-principles calculations to study pressure effects on the vibrational and superconducting properties of H 3 S in the cubic Im3m phase for the pressure range where the superconducting critical temperature (T c ) was measured (155-225 GPa). The pressure effects were incorporated using the Functional Derivative Method (FDM). In this paper, we present for the first time, the Cooper-Pairs Distribution Functions D cp (ω, T c ) for H 3 S, which will allow to identify the spectral regions where Cooper-Pairs formation at temperature T c is more favorable. We analyzed in detail the pressure effects on the electron-phonon spectral density function α 2 F(ω) and phonon density of states (PhDOS) and its relationship with the pressure dependence of the T c . Our results show a good agreement with the experiment. The D cp (ω, T c ) suggests that low frequency vibration region is where Cooper-Pairs are possible, which means that S-vibration have an important role in the H 3 S superconductivity properties. The increase in pressure leads to a reduction in the coupling constant λ and an increase in Coulomb pseudopotential µ * which induces a consistent correlation with T c , in good agreement with the Migdal-Eliashberg theory.

Cooper Pairs Distribution function for bcc Niobium under pressure from first-principles

“…Conventional superconductivity is explained by an attractive electron interaction through lattice vibrations, which is possible under a set of specific physical conditions. We can associate a probability of occurrence for each of them 8 – 10 . Thus, simultaneous likelihood summed over all electronic states defines a distribution function that establishes the spectral range where Cooper pairs could be formed.…”

“…Now, the probability that a pair of electrons is coupled by a phonon with energy between and is obtained by simultaneous likelihood, summed over all electronic states, that one electron with energy interacts with the lattice and transfers to it an energy , taking the state, and a second electron with energy , by interaction with the lattice, absorbs the phonon of energy and goes to state, at the temperature , ergo: where , namely Cooper Pairs Distribution function 9 , 10 , tells us the range of vibrational spectrum where the Cooper pairs are formed. Since electrons that form the Cooper pairs are near to the Fermi level , interacting through the lattice phonons, it implies that these are into energy interval.…”

Cooper-pair distribution function $$D_{cp}(\omega ,T_c)$$ for superconducting $$\hbox {D}_3\hbox {S}$$ and $$\hbox {H}_3\hbox {S}$$

“…In a previous theoretical work, Cooper-pair distribution function was reported 10 . This is a function built from the well-established Eliashberg spectral function and phonon density of states, which reveals information about the superconductor state through the determination of the spectral regions for Cooper pairs formation 11 .…”

“…Metallic hydrogen is a candidate to report a high critical temperature 3 , but it has not been obtained yet. However, several experimental and theoretical works have explored compounds where hydrogen is the main component 6 – 10 . Two of these compounds are and , of which experimental measurements showed values of 150 and 203 K 4 , respectively.…”

“…This is a function built from the well-established Eliashberg spectral function and phonon density of states, which reveals information about the superconductor state through the determination of the spectral regions for Cooper pairs formation 11 . The of compressed revealed that the low-frequency vibration region is where Cooper pairs are possible 10 . For bcc Niobium this function managed to simulate the Nb anomalies 11 measured at 5 and 50 GPa.…”