Tc of intermediate coupling superconductors with a variable electronic density of states (EDOS)

Using the model of Leavens and Carbotte for intermediate coupling superconductors, we have derived and evaluated analytical expressions for the critical temperature Tc, and the zero temperature gap Δ0 of those superconductors with a variable electronic density of states (EDOS). EDOS is given by a Lorentzian peak superimposed on a constant background with the chemical potential falling at some arbitrary position within the peak. The most significant modifications occur for a narrow Lorentzian with the peak close to the Fermi level. The value of the dimensionless ratio 2Δ0/kBTc remains close to the Bardeen–Cooper–Schrieffer (BCS) value of 3.53. Also, the present calculation compares very favourably with a previous exact calculation.

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Weak coupling superconductor with varying electronic density of states

Canadian Journal of Physics ◽

10.1139/p82-141 ◽

1982 ◽

Vol 60 (7) ◽

pp. 1029-1040 ◽

Cited By ~ 4

Author(s):

J. P. Carbotte ◽

A. Abd El-Rahman

Keyword(s):

Critical Temperature ◽

Density Of States ◽

Weak Coupling ◽

Chemical Potential ◽

Zero Temperature ◽

Electronic Density ◽

Electronic Density Of States ◽

Specific Heat Jump ◽

Analytic Expressions ◽

Arbitrary Position

Analytic expressions are derived and evaluated for the critical temperature (Tc) and the zero temperature gap edge (Δ0) of a weak coupling superconductor with a model electronic density of states: a Lorentzian superimposed on a constant background with Fermi energy falling at some arbitrary position within the peak. The shift in chemical potential, the gap edge near Tc, and the specific heat jump at Tc are also evaluated in closed form.

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Effects of energy dependence in the electronic density of states on some superconducting properties

Canadian Journal of Physics ◽

10.1139/p83-098 ◽

1983 ◽

Vol 61 (5) ◽

pp. 784-801 ◽

Cited By ~ 56

Author(s):

B. Mitrović ◽

J. P. Carbotte

Keyword(s):

Energy Dependence ◽

Density Of States ◽

Chemical Potential ◽

Numerical Solutions ◽

Tunneling Conductance ◽

Eliashberg Equations ◽

Electronic Density ◽

Electronic Density Of States ◽

Current Voltage ◽

Current Voltage Characteristics

We study the influence of energy dependence in the electronic density of states (EDOS) on the single particle tunneling characteristics into a superconductor. The Migdal–Eliashberg equations generalized to the case of a nonconstant EDOS are derived. Three equations are involved, one for the gap, another for the renormalization function, and a new one for the chemical potential shift which does not appear in the conventional formulation. Numerical solutions of these equations are obtained, from which current voltage characteristics are calculated for a model EDOS. The "inversion" of the calculated tunneling conductance shows that the effects of the peaks in the EDOS, on the scale of several Debye energies are important and cannot necessarily be reproduced within the usual Eliashberg theory by working with some effective value of electron–phonon spectral density α2(ω)F(ω) and/or Coulomb parameter μ* without introducing unphysical features to these parameters.

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Thermodynamics of weak coupling anisotropic superconductors with energy dependent electronic density of states

Canadian Journal of Physics ◽

10.1139/p83-102 ◽

1983 ◽

Vol 61 (6) ◽

pp. 825-837 ◽

Cited By ~ 3

Author(s):

H. G. Zarate ◽

J. P. Carbotte

Keyword(s):

Density Of States ◽

Thermodynamic Functions ◽

Weak Coupling ◽

Peak Width ◽

Significant Modification ◽

Electronic Density ◽

Electronic Density Of States ◽

Anisotropic Superconductors ◽

Energy Dependent ◽

Analytical Expressions

We derive analytical expressions for the gap edge and thermodynamic functions of anisotropic weak coupling superconductors with a model energy dependent electronic density of states N (ε). We choose N (ε) to be a Lorentzian superimposed on a constant background with the Fermi energy at an arbitrary distance from the maximum. Significant modification to the Bardeen–Cooper–Schrieffer (BCS) expressions are found for sharp peaks and for valleys in the density of states when the peak width is on the scale of the Debye energy. In this last case corrections can be very important.

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