Abstract
Within the general conformal transformation method a simplified analytical model is proposed to study the effect of external hydrostatic pressure on low- and high-temperature superconducting systems. A single fluctuation in the density of states, placed away from the Fermi level, as well as external pressure are included in the model to derive equations for the superconducting gap, free energy difference, and specific heat difference. The zero- and sub-critical temperature limits are discussed by the method of successive approximations. The critical temperature is found as a function of high external pressure. It is shown that there are four universal types of the response of the system, in terms of dependence of the critical temperature on increasing external pressure. Some effects, which should be possible to be observed experimentally in s-wave superconductors, the cuprates (i.e. high-Tc superconductors) and other superconducting materials of the new generation such as two-gap superconductors, are revealed and discussed. An equation for the ratio {{boldsymbol{ {mathcal R} }}}_{{bf{1}}} ≡ 2Δ(0)/Tc, as a function of the introduced parameters, is derived and solved numerically. Analysis of other thermodynamic quantities and the characteristic ratio {{boldsymbol{ {mathcal R} }}}_{{bf{2}}} ≡ ΔC(Tc)/CN(Tc) is performed numerically, and mutual relations between the discussed quantities are investigated. The simple analytical model presented in the paper may turn out to be helpful in searching for novel superconducting components with higher critical temperatures induced by pressure effects.
Highlights
A revival of theoretical studies on a new generation of superconducting materials has been recently brought by the discovery of iron-based superconductors[1,2]
In order to discuss the effect of high pressure on a superconducting system we use the conformal transformation method[40], that we have developed in our previous papers[3,6,7,8,27,43,44,45]
We have identified four universal types of the response of superconductors to an external high pressure, in terms of the dependence of the critical temperature on pressure
Summary
The superconducting state is formed in a fermion-carrier system that is located in the interior of a superconducting sample. In the sub-critical temperature range, i.e. forT Tc(χ), with the pressure included, we have to refer the discussion to the case p = 0, where x0 and κ are steady In this region, the magnitude of Δ(T, χ, x0, p)/2T is small and, in the first order of the perturbation method, Eq (9) can be transformed to the form ln ξp 2T ln 4eC π a. The normalized heat capacity jump exceeds the BCS value for χ > 0 and its magnitude remains smaller than the BCS value for χ < 0 If these superconductors were of type-(a) or -(b), there would need to exist some values of the external pressure for which the critical temperatures achieve their maximum or minimum, respectively. Note that in the superconducting state ΔF(T, χ, x0, p) given by Eq (23) must be negative, we demand the parameter χ > −1.279/φ(τ(x0 + κp)), remembering that φ(x) ≤ 1
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