New phenomenology from an old theory—The BCS theory of superconductivity revisited

Anghel, Dragos-Victor

doi:10.1016/j.physa.2019.121804

Cited by 7 publications

(12 citation statements)

References 30 publications

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“…In Refs. [1] , [2] , [3] a new procedure was proposed, which eventually imposes some consistency restriction over the standard formalism. The Hamiltonian

may be constructed using any parameter

–not necessary the chemical potential–and then it can be diagonalized, to bring it in the form (2).…”

Section: Methods Detailsmentioning

confidence: 99%

“…The energy gap and the quasiparticle populations are obtained by solving the coupled Eqs. (4) and (9) [1 , 2] . In the quasi-continuous limit, we assume constant density of states

.…”

Section: Methods Detailsmentioning

confidence: 99%

“…As in Ref. [2] , we write

where

, and

. The advantage of using the forms (12) is that when

(i.e., when

and

converge to either 0 or 1, depending on the signs of

and

.…”

Section: Methods Detailsmentioning

confidence: 99%

“… The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity has been revisited in a series of papers [1] , [2] , [3] and in this context the equation for the energy gap was generalized to a system of integral equations. The physical consequences of this change are major, leading not only to the change of the critical temperature and of energy gap, but even to a change of the order of the phase transition and to multiple solutions for the energy gap.…”

mentioning

confidence: 99%

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Methods of solving the system of equations for the energy gap in the revisited BCS theory of superconductivity

Anghel

Preda

2021

MethodsX

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The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity has been revisited in a series of papers [1] , [2] , [3] and in this context the equation for the energy gap was generalized to a system of integral equations. The physical consequences of this change are major, leading not only to the change of the critical temperature and of energy gap, but even to a change of the order of the phase transition and to multiple solutions for the energy gap. Nevertheless, finding the solutions of the proposed system of equations is much more complicated than solving the typical BCS gap equation and requires a careful analysis. This analysis is done here and consists of the following steps: writing the system of equations at finite temperature ( comparable with the energy gap ) and in the low temperature limit ( ); separate analysis of the equations and of their solutions in the two temperature ranges, (first) and (second) comparable with ; presenting the methods to consistenlty searching the solutions.

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“…In Refs. [1] , [2] , [3] a new procedure was proposed, which eventually imposes some consistency restriction over the standard formalism. The Hamiltonian

may be constructed using any parameter

–not necessary the chemical potential–and then it can be diagonalized, to bring it in the form (2).…”

Section: Methods Detailsmentioning

confidence: 99%

“…The energy gap and the quasiparticle populations are obtained by solving the coupled Eqs. (4) and (9) [1 , 2] . In the quasi-continuous limit, we assume constant density of states

.…”

Section: Methods Detailsmentioning

confidence: 99%

“…As in Ref. [2] , we write

where

, and

. The advantage of using the forms (12) is that when

(i.e., when

and

converge to either 0 or 1, depending on the signs of

and

.…”

Section: Methods Detailsmentioning

confidence: 99%

mentioning

confidence: 99%

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Methods of solving the system of equations for the energy gap in the revisited BCS theory of superconductivity

Anghel

Preda

2021

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“…See also Kuzemsky 22 , Chapters 26 and 29 and 23 , 24 . For the role of the chemical potential in the BCS-Bogoliubov model, see Anghel and Nemnes 25 and Anghel 26 , 27 .…”

Section: Introductionmentioning

confidence: 99%

An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature

Watanabe

2021

Sci Rep

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In the preceding papers the present author gave another proof of the existence and uniqueness of the solution to the BCS-Bogoliubov gap equation for superconductivity from the viewpoint of operator theory, and showed that the solution is partially differentiable with respect to the temperature twice. Thanks to these results, we can indeed partially differentiate the solution and the thermodynamic potential with respect to the temperature twice so as to obtain the entropy and the specific heat at constant volume of a superconductor. In this paper we show the behavior near absolute zero temperature of the thus-obtained entropy, the specific heat, the solution and the critical magnetic field from the viewpoint of operator theory since we did not study it in the preceding papers. Here, the potential in the BCS-Bogoliubov gap equation is an arbitrary, positive continuous function and need not be a constant.

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Multiple solutions for the equilibrium populations in BCS superconductors

Anghel

2021

Physica A: Statistical Mechanics and its Applications

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New phenomenology from an old theory—The BCS theory of superconductivity revisited

Cited by 7 publications

References 30 publications

Methods of solving the system of equations for the energy gap in the revisited BCS theory of superconductivity

Methods of solving the system of equations for the energy gap in the revisited BCS theory of superconductivity

An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature

Multiple solutions for the equilibrium populations in BCS superconductors

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