Simple analytical model of the effect of high pressure on the critical temperature and other thermodynamic properties of superconductors

Determination of pressure properties of superconducting systems based on characteristic ratios 2Δ(0)/Tc and ΔC(Tc)/CN(Tc)

A simplified analytical model of the effect of high pressure on the critical temperature and other thermodynamic properties of superconducting systems is developed using the general conformal transformation method and group-theoretical arguments. Relationships between the characteristic ratios \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal R} }_{1}\equiv 2{\rm{\Delta }}(0)/{T}_{{\rm{c}}}$$\end{document}ℛ1≡2Δ(0)/Tc and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal R} }_{2}\equiv {\rm{\Delta }}C({T}_{{\rm{c}}})/{C}_{{\rm{N}}}({T}_{{\rm{c}}})$$\end{document}ℛ2≡ΔC(Tc)/CN(Tc) and the stability of the superconducting state is discussed. Including a single two-parameter fluctuation in the density of states, placed away from the Fermi level, stable solutions determined by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ {\mathcal R} }_{1}$$\end{document}ℛ1 are found. It is shown that the critical temperature T_c(p), as a function of high external pressure, can be predicted from experimental data, based on the values of the two characteristic ratios, the critical temperature, and a pressure coefficient measured at zero pressure. The model can be applied to s-wave low-temperature and high-temperature superconductors, as well as to some novel superconducting systems of the new generation. The problem of emergence of superconductivity under high pressure is explained as well. The discussion is illustrated by using experimental data for superconducting elements available in the literature. A criterion for compatibility of experimental data is formulated, allowing one to identify incompatible measurement data for superconducting systems for which the maximum or the minimum critical temperature is achieved under high pressure.