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Title: Elaboration of the α-model derived from the BCS theory of superconductivity

Abstract

The single-band α-model of superconductivity (Padamsee et al 1973 J. Low Temp. Phys. 12 387) is a popular model that was adapted from the single-band Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity mainly to allow fits to electronic heat capacity versus temperature T data that deviate from the BCS prediction. The model assumes that the normalized superconducting order parameter Δ(T)/Δ(0) and therefore the normalized London penetration depth λL(T)/λL(0) are the same as in BCS theory, calculated using the BCS value αBCS ≈ 1.764 of α ≡ Δ(0)/kBTc, where kB is The single-band α-model of superconductivity (Padamsee et al 1973 J. Low Temp. Phys. 12 387) is a popular model that was adapted from the single-band Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity mainly to allow fits to electronic heat capacity versus temperature T data that deviate from the BCS prediction. The model assumes that the normalized superconducting order parameter Δ(T)/Δ(0) and therefore the normalized London penetration depth λL(T)/λL(0) are the same as in BCS theory, calculated using the BCS value αBCS ≈ 1.764 of α ≡ Δ(0)/kBTc, where kB is Boltzmann's constant and Tc is the superconducting transition temperature. On the other hand, to calculate the electronic free energy, entropy, heat capacity and thermodynamicmore » critical field versus T, the α-model takes α to be an adjustable parameter. Here we write the BCS equations and limiting behaviors for the superconducting state thermodynamic properties explicitly in terms of α, as needed for calculations within the α-model, and present plots of the results versus T and α that are compared with the respective BCS predictions. Mechanisms such as gap anisotropy and strong coupling that can cause deviations of the thermodynamics from the BCS predictions, especially the heat capacity jump at Tc, are considered. Extensions of the α-model that have appeared in the literature, such as the two-band model, are also discussed. Tables of values of Δ(T)/Δ(0), the normalized London parameter Λ(T)/Λ(0) and λL(T)/λL(0) calculated from the BCS theory using α = αBCS are provided, which are the same in the α-model by assumption. Tables of values of the entropy, heat capacity and thermodynamic critical field versus T for seven values of α, including αBCS, are also presented.« less

Authors:
Publication Date:
Research Org.:
Ames Lab., Ames, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1132290
Report Number(s):
IS-J 8194
Journal ID: ISSN 0953-2048
DOE Contract Number:  
DE-AC02-07CH11358
Resource Type:
Journal Article
Journal Name:
Superconductor Science and Technology
Additional Journal Information:
Journal Volume: 26; Journal Issue: 11; Journal ID: ISSN 0953-2048
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Johnston, David C. Elaboration of the α-model derived from the BCS theory of superconductivity. United States: N. p., 2013. Web. doi:10.1088/0953-2048/26/11/115011.
Johnston, David C. Elaboration of the α-model derived from the BCS theory of superconductivity. United States. https://doi.org/10.1088/0953-2048/26/11/115011
Johnston, David C. 2013. "Elaboration of the α-model derived from the BCS theory of superconductivity". United States. https://doi.org/10.1088/0953-2048/26/11/115011.
@article{osti_1132290,
title = {Elaboration of the α-model derived from the BCS theory of superconductivity},
author = {Johnston, David C.},
abstractNote = {The single-band α-model of superconductivity (Padamsee et al 1973 J. Low Temp. Phys. 12 387) is a popular model that was adapted from the single-band Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity mainly to allow fits to electronic heat capacity versus temperature T data that deviate from the BCS prediction. The model assumes that the normalized superconducting order parameter Δ(T)/Δ(0) and therefore the normalized London penetration depth λL(T)/λL(0) are the same as in BCS theory, calculated using the BCS value αBCS ≈ 1.764 of α ≡ Δ(0)/kBTc, where kB is The single-band α-model of superconductivity (Padamsee et al 1973 J. Low Temp. Phys. 12 387) is a popular model that was adapted from the single-band Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity mainly to allow fits to electronic heat capacity versus temperature T data that deviate from the BCS prediction. The model assumes that the normalized superconducting order parameter Δ(T)/Δ(0) and therefore the normalized London penetration depth λL(T)/λL(0) are the same as in BCS theory, calculated using the BCS value αBCS ≈ 1.764 of α ≡ Δ(0)/kBTc, where kB is Boltzmann's constant and Tc is the superconducting transition temperature. On the other hand, to calculate the electronic free energy, entropy, heat capacity and thermodynamic critical field versus T, the α-model takes α to be an adjustable parameter. Here we write the BCS equations and limiting behaviors for the superconducting state thermodynamic properties explicitly in terms of α, as needed for calculations within the α-model, and present plots of the results versus T and α that are compared with the respective BCS predictions. Mechanisms such as gap anisotropy and strong coupling that can cause deviations of the thermodynamics from the BCS predictions, especially the heat capacity jump at Tc, are considered. Extensions of the α-model that have appeared in the literature, such as the two-band model, are also discussed. Tables of values of Δ(T)/Δ(0), the normalized London parameter Λ(T)/Λ(0) and λL(T)/λL(0) calculated from the BCS theory using α = αBCS are provided, which are the same in the α-model by assumption. Tables of values of the entropy, heat capacity and thermodynamic critical field versus T for seven values of α, including αBCS, are also presented.},
doi = {10.1088/0953-2048/26/11/115011},
url = {https://www.osti.gov/biblio/1132290}, journal = {Superconductor Science and Technology},
issn = {0953-2048},
number = 11,
volume = 26,
place = {United States},
year = {Mon Oct 14 00:00:00 EDT 2013},
month = {Mon Oct 14 00:00:00 EDT 2013}
}