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

We study the effects of energy dependence in the electronic density of states (EDOS) on the electron quasiparticle properties in the normal state. The Migdal–Eliashberg equations generalized to include a nonconstant EDOS are derived in the isotropic approximation. By numerical solution of the electron self-energy equations in the normal state, we assess the effect of the interplay of the energy dependence in the EDOS, the electron–phonon interaction, and/or elastic impurity scattering on the electron quasiparticle properties. Self-consistency requirements are fully discussed.

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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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Free energy formula for a strong coupling superconductor with energy dependent electronic density of states

Canadian Journal of Physics ◽

10.1139/p83-107 ◽

1983 ◽

Vol 61 (6) ◽

pp. 872-887 ◽

Cited By ~ 18

Author(s):

B. Mitrovic ◽

J. P. Carbotte

Keyword(s):

Free Energy ◽

Density Of States ◽

Impurity Scattering ◽

Energy Difference ◽

Critical Magnetic Field ◽

Half Width ◽

Electronic Density ◽

Electronic Density Of States ◽

Strong Coupling Superconductor ◽

Energy Dependent

Generalized expressions for the free energy difference between normal and superconducting states are derived for the case of an energy dependent (ED) electronic density of states (EDOS) with normal and paramagnetic impurity scattering included. The derivation starts from the Eliashberg expression for the grand thermodynamic potential and ends in explicit formulas for the case of a symmetric Lorentzian model EDOS. Some numerical results are given for the critical magnetic field deviation function and the ratio 2Δ0/kBTc of the Δ0 to the critical temperature Tc. For a peak at the Fermi energy of half width less than the Debye energy (ωD), the modified Eliashberg theory is needed to describe its effect on the thermodynamic properties, whereas for a half width greater than ωD, the corrections to a flat approximation are small.

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