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- Title
On the Generalized BCS Equations Incorporating Chemical Potential for the T<sub>c</sub> and the Calculation of the Coherence Length of Some Elements and Compressed H<sub>3</sub>S.
- Authors
Malik, G. P.; Varma, V. S.
- Abstract
The BCS equations do not contain the Fermi energy (EF) because they are derived under the assumption EF >> k θ, where k is the Boltzmann constant and θ the Debye temperature of the superconductor (SC). There is a need to do away with this assumption because of the current belief that it is not valid for many SCs, including the high-Tc SCs. We present here the EF -incorporated generalized BCS equations (GBCSEs) for the Tcs and the gaps (Δs) of both elemental and composite SCs. A virtue of this approach is that it leads to an unambiguous definition of the BCS coherence length ξ0 = ξ0 (Δ0(EF), vF), where vF is the Fermi velocity corresponding to a specific value of EF associated with the Δ of the SC at zero temperature. The SCs for which the GBCSEs have been employed in this paper are: Sn, Al, Pb, Cd, Nb and compressed H3S. While the value of ξ0 for H3S thus obtained agrees with its value obtained by a variety of different methods, its values for the elemental SCs considered here differ from those given in standard texts. We give here a detailed explanation of this mismatch and how the situation may be remedied.
- Subjects
CHEMICAL potential; CHEMICAL equations; DEBYE temperatures; BOLTZMANN'S constant; FERMI energy
- Publication
Journal of Low Temperature Physics, 2023, Vol 211, Issue 1/2, p45
- ISSN
0022-2291
- Publication type
Article
- DOI
10.1007/s10909-023-02938-6