Energy-Gap Function in the Theory of Superconductivity

1963 ◽  
Vol 131 (1) ◽  
pp. 73-78 ◽  
Author(s):  
James C. Swihart
Keyword(s):  
Energy Gap ◽  
Gap Function ◽  
Theory Of Superconductivity

On a General Formula for the Transition Temperature of Superconductors

1974 ◽  
Vol 29 (3) ◽  
pp. 445-451 ◽  
Author(s):  
W. Kessel
Keyword(s):  
Transition Temperature ◽  
Integral Equations ◽  
General Formula ◽  
Transition Point ◽  
Energy Gap ◽  
Eliashberg Equations ◽  
Operator Form ◽  
Method Of Solution ◽  
Theory Of Superconductivity ◽  
Phonon Properties

A method of solution of the Eliashberg equations in the theory of superconductivity is derived which uses the fact that near the transition point the energy gap is small compared to the energies over which the electron-phonon properties vary appreciably. On this basis the Eliashberg equations are converted into linear inhomogeneous integral equations. Their solution is given in operator form and provides a general formula for the transition temperature

An electron tunneling investigation of quench-condensed superconductors

1970 ◽  
Vol 48 (23) ◽  
pp. 2783-2803 ◽  
Author(s):  
J. D. Leslie ◽  
J. T. Chen ◽  
T. T. Chen
Keyword(s):  
Transition Temperature ◽  
Energy Function ◽  
Phonon Spectrum ◽  
Energy Gap ◽  
Electron Tunneling ◽  
Coupling Theory ◽  
Complex Energy ◽  
Self Energy ◽  
Coulomb Pseudopotential ◽  
Theory Of Superconductivity

An electron tunneling investigation has been carried out on quench-condensed Bi, Ga, Pb, Pb∙75Bi∙25, Pb∙50Bi∙50, and Pb∙25Bi∙75. The energy gap and transition temperature have been measured for each sample. The tunneling derivative data have been analyzed in terms of the strong-coupling theory of superconductivity by means of a computer program of W. L. McMillan. The effective phonon spectrum, the Coulomb pseudopotential, the complex energy gap function, the pairing self-energy function, and the electron renormalization function have been determined for each sample. Certain parameters based on integrals over the phonon spectrum have also been calculated for each sample.

The Gap Function in YBa2Cu3O7

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3057-3062 ◽  
Author(s):  
G. L. Zhao ◽  
D. Bagayoko
Keyword(s):  
Electronic Structure ◽  
Transition Temperature ◽  
Energy Gap ◽  
Electronic States ◽  
Gap Function ◽  
Interaction Matrix ◽  
Matrix Elements ◽  
Phonon Interaction ◽  
Gap Equation ◽  
Electron Phonon Interaction

We have solved the four-dimensional anisotropic Eliashberg gap equation for YBa2Cu3O7 (YBCO) using the calculated electronic structure and the electron–phonon interaction matrix elements. The calculated T c for YBCO is about 89 K or μ*= 0.1. At or slightly above the transition temperature T c , the real part of the gap function Δ(k, 0), for all the k-points on the Fermi surface, becomes zero and the material is not superconducting. However, the energy gap function Δ(k,ω) is still nonzero for ω > 0 for some electronic states, leading to a pseudo-gap behavior in YBCO.

Role of superconducting energy gap in extended BCS-Bose crossover theory

2017 ◽  
Vol 31 (25) ◽  
pp. 1745004 ◽  
Author(s):  
I. Chávez ◽  
L. A. García ◽  
M. de Llano ◽  
M. Grether
Keyword(s):  
Energy Gap ◽  
Einstein Condensation ◽  
Cooper Pairs ◽  
Number Density ◽  
Superconducting Energy Gap ◽  
Special Cases ◽  
Bose Einstein ◽  
Hole Cooper Pairs ◽  
Theory Of Superconductivity

The generalized Bose–Einstein condensation (GBEC) theory of superconductivity (SC) is briefly surveyed. It hinges on three distinct new ingredients: (i) Treatment of Cooper pairs (CPs) as actual bosons since they obey Bose statistics, in contrast to BCS pairs which do not obey Bose commutation relations; (ii) inclusion of two-hole Cooper pairs (2hCPs) on an equal footing with two-electron Cooper pairs (2eCPs), thus making this a complete boson–fermion (BF) model; and (iii) inclusion in the resulting ternary ideal BF gas with particular BF vertex interactions that drive boson formation/disintegration processes. GBEC subsumes as special cases both BCS (having its 50–50 symmetry of both kinds of CPs) and ordinary BEC theories (having no 2hCPs), as well as the now familiar BCS-Bose crossover theory. We extended the crossover theory with the explicit inclusion of 2hCPs and construct a phase diagram of [Formula: see text] versus [Formula: see text], where [Formula: see text] and [Formula: see text] are the critical and Fermi temperatures, [Formula: see text] is the total number density and [Formula: see text] that of unbound electrons at [Formula: see text]. Also, with this extended crossover one can construct the energy gap [Formula: see text] versus [Formula: see text] for some elemental SCs by solving at least two equations numerically: a gap-like and a number equation. In 50–50 symmetry, the energy gap curve agrees quite well with experimental data. But ignoring 2hCPs altogether leads to the gap curve falling substantially below that with 50–50 symmetry which already fits the data quite well, showing that 2hCPs are indispensable to describe SCs.

PECULIARITY OF SUPERCONDUCTIVITY IN A METAL WITH A SPIRAL MAGNETIC STRUCTURE

1990 ◽  
Vol 04 (03) ◽  
pp. 447-472 ◽  
Author(s):  
YU. A. IZYUMOV ◽  
V. M. LAPTEV
Keyword(s):  
Magnetic Structure ◽  
Exchange Coupling ◽  
Magnetic Ordering ◽  
Direct Consequence ◽  
Gap Function ◽  
Superconducting Transition ◽  
Conduction Electrons ◽  
Reversal Invariance ◽  
Spiral Magnetic Structure ◽  
Theory Of Superconductivity

Superconductivity states in a metal with existing spiral magnetic structure is studied. s-d exchange interaction of the conduction electrons with localized spins forming the magnetic ordering is treated in the framework of the strong coupling theory of superconductivity. Two separate factors are taken into account which influence the possibility of coexistence of superconductivity and magnetic ordering: electron-magnon interaction, as well as a modification of the electron spectrum due to its interaction with the static magnetic structure. The gap function is a 2 × 2 matrix with respect to the band indexes of hybridized electron states with up and down spins. The linearized Eliasberg's type equations for diagonal and off-diagonal elements are separated. Off-diagonal and diagonal elements correspond to quasisinglet and quasitriplet pairings respectively. As a direct consequence of violation of the time reversal invariance due to magnetic ordering, the diagonal gap function does not have a definite parity with respect to frequency. For this situation a moment method is developed for a calculation of the superconducting transition temperature in the limit of weak s-d-exchange coupling.

scholarly journals Superfluid Density and Energy Gap Function of SuperconductingPrPt4Ge12

2009 ◽  
Vol 103 (14) ◽  
Author(s):  
A. Maisuradze ◽  
M. Nicklas ◽  
R. Gumeniuk ◽  
C. Baines ◽  
W. Schnelle ◽  
...  
Keyword(s):  
Energy Gap ◽  
Superfluid Density ◽  
Gap Function
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