Variations of Cutoff Phonon Frequencies in Strong-Coupling Superconductors

  • A. Rothwarf
  • F. Rothwarf
  • C. T. Rao
  • L. W. Dubeck


The ratio 2△/kT c , where △ is the zero-temperature energy gap and T c is the transition temperature, is commonly used to indicate whether a superconductor is a strong-or weak-coupling material. Recently Laibowitz, Sadagopan, and Seiden’ (LSS) have analyzed the data for a number of elements and alloys and claimed that the theoretical expression for 2△/kT c , derived by Geilikman and Kresin2 (GK) cannot explain their data. The GK expression is
$$2\Delta /k{{T}_{C}}=3.53\left[ 1+5.3{{\left( {{T}_{_{c}/}}a{{\theta }_{D}} \right)}^{2}}In\left( a{{\theta }_{D}}/{{T}_{c}} \right) \right]$$
where a is a constant which relates the cutoff energy in the BCS theory to the Debye temperature, and is usually assumed to be of order unity (GK suggest a ∼0.7 for lead). To fit existing data, LSS proposed the empirical expression
$$2\Delta /k{{T}_{c}}=3.5\left[ 1+b\exp \left( C{{T}_{c}}/{{\theta }_{D}} \right) \right]$$
with b = 0.78 × 10−3 and C = 114


Debye Temperature Transverse Mode Empirical Expression Transverse Phonon Brillouin Zone Boundary 
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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • A. Rothwarf
    • 1
  • F. Rothwarf
    • 2
  • C. T. Rao
    • 3
  • L. W. Dubeck
    • 3
  1. 1.School of Metallurgy and Materials ScienceUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.U.S. Army Electronics Technology and Devices Laboratory (ECOM)Fort MonmouthUSA
  3. 3.Physics DepartmentTemple University PhiladelphiaUSA

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