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The Form of Energy Gap and Critical Temperature of Superconductor Implied by Fluctuations of Density of States

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Gładysiewicz M., Gonczarek R., Mulak M.

Acta Physica Polonica A

2000

vol. 97

issue 6

1039-1051

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}.

The Form and Properties of the Tight-Binding Density of States in Two Dimensions. Possible Application to Superconductivity

100%

Gładysiewicz M., Gonczarek R., Mulak M.

Acta Physica Polonica A

2002

vol. 101

issue 6

865-874

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.

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2 Acta Physica Polonica A

1 2002

1 2000

2 Gonczarek R.

2 Gładysiewicz M.

2 Mulak M.

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The Form of Energy Gap and Critical Temperature of Superconductor Implied by Fluctuations of Density of States

The Form and Properties of the Tight-Binding Density of States in Two Dimensions. Possible Application to Superconductivity