Relation between Superconducting Energy Gaps and Critical Magnetic Fields

  • D. U. Gubser
  • R. A. Hein


In 1965 Toxen noted1 that for most elemental superconductors there exists a linear relation between the initial slope of the reduced critical magnetic field curve and the zero-temperature energy gap:
$$-({{T}_{0}}/{{H}_{0}}){{(d{{H}_{c}}/dT)}_{T}}{{_{=}}_{T}}_{_{0}}\equiv -{{(dh/dt)}_{t}}_{=1}=\vartriangle /k{{T}_{0}}$$
where T0 is the superconducting transition temperature, H c is the critical magnetic field [H oH c (T = 0)], and 2∆ is the zero-temperature energy gap. According to weak coupling BCS theory,2
$$\Delta /k{{T}_{0}}=1.016{{(dh/dt)}_{t}}{{=}_{1}}$$
where (dh/dt) t = 1 and ∆/kT0 are not variables but are fixed numbers, 1.737 and 1.764, respectively. The importance of Toxen’s observation is that the weak coupling BCS expression is found to hold for moderate and strong coupling superconductors provided (dh/dt) t=1 and ∆/k T0 are treated as variables. One can therefore determine ∆ if T 0 , H 0 , and \({\left( {d{H_c}/dT} \right)_{T = {T_0}}}\) are known.


Weak Coupling Superconducting Transition Temperature Critical Magnetic Field Specific Heat Data Valid Expression 
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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • D. U. Gubser
    • 1
    • 1
  • R. A. Hein
    • 1
    • 1
  1. 1.Naval Research LaboratoryUSA

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