Thermal Conductivity in the TwoBand Model of Superconducting Transition Metals Containing Nonmagnetic Impurities
Abstract
Using the Green'sfunction formulation, an expression has been derived for the thermal conductivity of transitionmetal superconductors containing nonmagnetic impurities in the twoband model of Suhl, Matthias, and Walker (SMW). The calculations have been carried out neglecting the interband electronphonon coupling and taking the interbandscattering collision time τ_{sd}~10^{12} sec. The thermal conductivity K is found to be the sum of two terms K_{1} and K_{2}. K_{1} is the dominating term and depends in a complicated manner on both energy gap parameters Δ¯_{s} and Δ¯_{d}, due to s and d bands, respectively. On the other hand, K_{2} depends only on Δ¯_{d} and is smaller by a factor of ~10^{7}. A loglog plot of thermal conductivity vs temperature turns out to be a straightline curve with a slight change in its slope at a temperature which depends upon the impurity concentration. Furthermore, K is found to decrease with increase in impurity concentration. These qualitative features of the present study are in very good agreement with the recent experimental investigations of Anderson et al. on niobium and lend support to the validity of the SMW twobandmodel theory.
 Publication:

Physical Review B
 Pub Date:
 October 1972
 DOI:
 10.1103/PhysRevB.6.2642
 Bibcode:
 1972PhRvB...6.2642K