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1
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Discontinuous Phase Transitions in S-Paired Fermi Systems

100%
Mulak M., Gonczarek R.
Acta Physica Polonica A
|
1997
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vol. 92
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issue 6
1177-1189
EN
The most general S-paired systems of fermions for which a gap equation can be separated according to the specific redefined variables, are considered. Moreover, a solution of this gap equation (gap energy) is obtained in a parametric form. It allows us to investigate thermodynamic properties of such systems i.e. the thermodynamic potential, entropy, heat capacity and critical magnetic induction. We show also that the heat capacity difference between the superconducting and the normal phase is entirely determined by the order parameter. The obtained results reveal possibilities of discontinuous phase transition to the normal state and moreover, the theorem on existence of such transitions is formulated and proved. The condition for the BCS-type energy gap is given, which additionally classifies properties of the heat capacity of S-paired phase by virtue of the shape of the energy gap. In order to illustrate the developed formalism, the numerical results for the so-called statistical spin liquids and application of the established methods to the experimental data conversion, are presented and discussed.
2
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Structures of Thermodynamic Functions for S-Paired Fermi Systems in Parametric Equations Approach

100%
Mulak M., Gonczarek R.
Acta Physica Polonica A
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1996
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vol. 89
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issue 5-6
689-698
EN
The general method of investigation of S-paired Fermi systems is given and discussed as generalization of parametric equation for the energy gap. The additional parametric equations for thermodynamic potential and heat capacity are obtained as functions of introduced parameters. The detailed calculations are given for a few exemplary chosen magnetic fields and superflows. Moreover, we consider the case of so-called statistical spin liquid, which constitutes non-BCS model.
3
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Parametric Equations for the Energy Gap. Extended BCS Case

100%
Gonczarek R., Mulak M.
Acta Physica Polonica A
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1994
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vol. 86
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issue 6
1007-1014
EN
The generalised form of the gap equation which comprises also some non-BCS approaches is defined and solved. The parametric gap equations have been derived in a few equivalent cases and discussed in_{}dissimilar limits. It is shown that the relations between the critical temperature and zero-temperature energy gap can be extended for all systems under consideration. The main benefits and incontestable advantage of the presented method are demonstrated with regard to the general BCS case.
4
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Conditions for the Cooper Pair Creation in 2- up to 3-Dimensional Fermi Liquids

100%
Gonczarek R., Mulak M.
Acta Physica Polonica A
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1994
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vol. 86
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issue 6
929-938
EN
We reconsider the Pfitzner and Wölfle results concerning the quasi-particle scattering amplitude in Fermi liquid and adopt them to the sufficiently low-temperature and flat-confined systems, where solely two types of quasi--particle interactions are permitted. We find relations between the pairing interaction and Landau parameters and establish plain criteria for the creation of singlet or triplet Cooper pairs. Moreover, we present methods allowing us to estimate values of interaction parameters and transition temperatures in flat-confined systems basing on their bulk parameters. The obtained results are in agreement with experimental data for helium-3 and its films and explain an absence of superconductivity in alkali metals.
5
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Thermodynamic Properties of D-Wave Paired Superconductors

81%
Gonczarek R., Mulak M., Kumala W.
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vol. 95
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issue 2
231-242
EN
The D-wave paired Fermi system is considered in the frame of generalized gap equation obtained in a BCS-like approach. It is shown that the thermodynamic functions of a system, as the thermodynamic potential, entropy and heat capacity differences between the normal and superconducting state are precisely defined functionals of the energy gap as a function of temperature. The derived formulas are identical as those obtained for S-wave paired Fermi system. It states that the developed formalism can be applied, in practice, to investigation of real superconductors in which a singlet state is realized. Some numerical results illustrating prospects and capabilities of the presented formalism are given for chosen structures of the order parameter.
6
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The Form of Energy Gap and Critical Temperature of Superconductor Implied by Fluctuations of Density of States

81%
Gładysiewicz M., Gonczarek R., Mulak M.
Acta Physica Polonica A
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2000
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vol. 97
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issue 6
1039-1051
EN
The s-paired BCS superconductor with the electron density of states depending on energy in the vicinity of Fermi level is considered. The existence of such fluctuations of electron density of states may be referred to Van Hove singularities widely discussed in the literature. In the paper three types of small fluctuations of the electron density of states introduced about its average background's value are analysed: Lorentzian, triangle, and logarithmic ones. In order to calculate numerically the energy gap and critical temperature, the formalism of parametric BCS gap equations is applied. The positive fluctuations (peaks) correspond to the increase in occupied states number inducing a higher critical temperature. On the other hand, negative fluctuations, which decrease the number of occupied states, lead to a lower critical temperature. Such decrease in critical temperature can lead, at a specific choice of parameters, to the decease in superconductivity. The presence of fluctuations finds reflection in the shape of energy gap as a function of temperature. In the vicinity of T=0 an abrupt decrease or increase in the energy gap to the original BCS value, according to the sign of the fluctuation, is observed. In turn, the fluctuations do not change the behaviour of the energy gap near T_{c}.
7
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The Form and Properties of the Tight-Binding Density of States in Two Dimensions. Possible Application to Superconductivity

81%
Gładysiewicz M., Gonczarek R., Mulak M.
Acta Physica Polonica A
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2002
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vol. 101
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issue 6
865-874
EN
The form of the density of states for a tight-binding model with the first and the next-nearest neighbour hoppings for a rectangular planar lattice and a shift of the chemical potential are calculated. This is newly and comprehensively formulated integral form illustrated numerically, helpful in approach to two-dimensional superconducting models. In some particular cases the complete analytical forms of the density of states are obtained. It is shown that for all cases the density of states has a single van Hove singularity of the logarithmic type at the identically defined point. The proper approximate analytical representations are found. The difference between the exact numerical and approximate analytical forms is evaluated and illustrated.
8
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Thermodynamic Properties of D-Wave Paired Superconductors in the Low Temperature and Subcritical Regions

81%
Kumala W., Gonczarek R., Mulak M.
Acta Physica Polonica A
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2000
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vol. 97
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issue 4
693-703
EN
D-wave paired isotropic Fermi system in the limiting cases T → T_{c} and T → 0 is considered. Values of the energy gap, the thermodynamic potential, and the specific heat as a function of temperature are given for admissible solutions and compared with values for S-wave paired system. It is shown that the linear term of low temperature specific heat vanishes likewise in case of S-wave pairing. The obtained results make prospects to define the geometry of the energy gap in virtue of the behavior of the specific heat in the limiting temperature cases for heavy-fermion superconductors.
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