Ultrasonic Absorption in Superconducting Single Crystals of Nb_{1 − x} Mo _x

Abstract

The measurement of ultrasonic absorption by the conduction band electrons has frequently been used to determine the superconducting energy gap Δ(T). In general, the experiments performed on many of the elemental superconductors in the clean state (i.e., ξ₀/l < 1, where l is the electron mean free path and ξ₀ is the BCS coherence length) tend to support the BCS¹ prediction

$${{{\alpha }_{s}}}/{{{\alpha }_{n}}}\;=2{{\left( {{e}^{{\Delta }/{kT}\;}}+1 \right)}^{-1}}$$

(1)

Discrepancies from Eq. (1) have, however, been reported for a number of high-purity elements such as the type I superconductor Sn² and the type II superconductor Nb.^3–6 Only a few attenuation measurements have been made on superconducting alloys in the dirty regime(i.e.,ξ₀/l > 1) due to the difficulty of measuring the electron attenuation, which is often overshadowed by the background absorption α _B . Tittman⁷ has shown the validity of Eq. (1) for the type II superconductor V-5.6 at.% Ta in the dirty regime ξ₀/l ≈ 5) assuming a BCS gap parameter A≡ 2Δ(0)/kT _c ≈ 3.6. It is therefore expected that Eq. (1) should describe attenuation measurements for superconducting alloys, or at least it should apply in the dirty limit ξ₀/l ≫ 1.