Mateusz Krzyzosiak

Some universal relations between the gap and thermodynamic functions plausible for various models of superconductors

It is proven that there exist some universal relations between the energy gap and the differences of the thermodynamic potential, entropy, specific heat and critical magnetic field for many two- and three-dimensional models of superconductivity with spin-singlet Cooper pairs forming \textit{s} or \textit{d} or \textit{g} etc. states. The obtained formulae make it possible to derive thermodynamic functions and, in particular, the superconducting specific heat and the critical magnetic induction in the whole temperature range

Electromagnetic response in kinetic energy driven cuprate superconductors: Linear response approach

0\leq T\leq T_{c}

ON A MODEL OF SUPERCONDUCTIVITY REALIZED IN THE METALLIC PHASE OF STRONGLY CORRELATED ELECTRONS REVEALING A FIRST-ORDER PHASE TRANSITION

employing the form of

New classes of integrals inherent in the mathematical structure of extended equations describing superconducting systems

\Delta(T)

On New Families of Integrals in Analytical Studies of Superconductors within the Conformal Transformation Method

only. The inverse formula allowing us to find

Interplay between spin-singlet and spin-triplet order parameters in a model of an anisotropic superconductor with cuprate planes

\Delta(T)

THE SUPERCONDUCTING STATE OF A SINGULAR FERMI LIQUID IN A MAGNETIC FIELD

, when the temperature dependence of the specific heat difference is known, is also presented. The results are referred to some obtained within the McMillan formalism, and some remarks on an application of the present formulae to the {\textit{t--J}} model are given.

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

Within the framework of the kinetic energy driven superconductivity, the electromagnetic response in cuprate superconductors is studied in the linear response approach. The kernel of the response function is evaluated and employed to calculate the local magnetic field profile, the magnetic field penetration depth, and the superfluid density, based on the specular reflection model for a purely transverse vector potential. It is shown that the low temperature magnetic field profile follows an exponential decay at the surface, while the magnetic field penetration depth depends linearly on temperature, except for the strong deviation from the linear characteristics at extremely low temperatures. The superfluid density is found to decrease linearly with decreasing doping concentration in the underdoped regime. The problem of gauge invariance is addressed and an approximation for the dressed current vertex, which does not violate local charge conservation is proposed and discussed.

Singular Fermi liquid as a model of unconventional superconductivity: Thermodynamic and magnetic properties

Model of superconductivity in the metallic phase of strongly correlated electrons in a half-filled narrow band forming a paramagnetic spin liquid is presented. A qualitatively new ground state and other eigenstates for the superconducting phase are found. Thermodynamic functions are derived within the Bogolubov method. Analytical formulae for the free energy as well as the gap equation and the equation for the chemical potential are presented. It is shown that the energy gap and the chemical potential are mutually correlated functions which must be simultaneously derived in a self-consistent manner. The gap equation and the equation for the chemical potential are numerically solved. The energy gap is doubly-valued in the subcritical temperature region, however only for the higher values of the gap the superconducting phase is stable. The phase transition between the superconducting and the normal phase is found to be of the first order with a conspicuous discontinuity in the entropy. Moreover it is shown that the derivation of the superconducting specific heat from the thermodynamic potential difference requires to include a chemical potential contribution.

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper, we discuss the mathematical structure of the s-wave superconducting gap and other quantitative characteristics of superconducting systems. In particular, we evaluate and discuss integrals inherent in fundamental equations describing superconducting systems. The results presented here extend the approach formulated by Abrikosov and Maki, which was restricted to the first-order expansion. A few infinite families of integrals are derived and allow us to express the fundamental equations by means of analytic formulas. They can be then exploited in order to find some quantitative characteristics of superconducting systems by the method of successive approximations. We show that the results can be applied to some modern formalisms in order to study high-Tc superconductors and other superconducting materials of the new generation.