Anomalous Ultrasonic Attenuation in Pure Superconducting Nb

Lacy, L. L.; Daniel, A. C.

doi:10.1103/physrevlett.27.1128

Cited by 19 publications

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“…1) is 2A(0) = (3.52 ± 0.02)kT c , in agreement with that found previously 13 on a less pure sample and in reasonable agreement with an extrapolation of the results by Lacy and Daniel, 9 for propagation along the [100] direction. With the use of Eq.…”

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Ultrasonic Evidence Against Multiple Energy Gaps in Superconducting Niobium

1972

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extended the BCS theory of superconductivity to the case of two overlapping electron bands and suggested that this might apply to pure superconducting transition metals such as Nb. They postulated that each band could have distinct superconducting energy gaps and possibly different transition temperatures, depending on the strength of the interband and intraband couplings. Experimental evidence for two energy gaps in Nb came from the heat-capacity data of Shen, Senozan, and Phillips, 2 which were interpreted 3 in terms of a dband gap 2A d (0) = 3.5&T C and an s-band gap 2A 5 (0) = 0.32kT c . The ratio of the density of states at the Fermi level, N s /N d , depended on the purity of the sample and was 0.015 when the residual resistivity ratio (RRR) was 110. Direct evidence for the small energy gap has also come from tunneling experiments on pure Nb crystals. Hafstrom and MacVicar 4 deduced an energy gap 2A(0) =0.37&T C from the tunneling characteristics along many directions (with the notable exception of the [100] direction). Thermal-conductivity measurements 5 on pure Nb were initially interpreted 5,6 on a two-gap model, but later data led Anderson, Satterthwaite, and Smith 7 to conclude b H. Kolbenstvedt, J. Appl. Phys. 38, 4785 (1967). . that they provided no evidence for a second gap, and put an upper limit on N s /N d -10 " 3 for a sample with an RRR of 2000.Recently, ultrasonic attenuation measurements 8 ' on superconducting Nb have been analyzed in terms of a two-gap model. However, the energy gaps required to fit the data were quite different. At low temperatures the usual BCS gap 2A 1 (0) = 3.5&T C applied, but near T c a large gap 2A 2 (0) -10kT c was used. This large gap was purity dependent, increasing as the sample RRR increased. These two gaps were associated by Lacy and Daniel 9 with the s and d bands, in contrast to the previous analyses, 3 ' 4 where the s-band gap was very small. Here we report measurements of the electronic attenuation in the normal state, a n9 and in the superconducting state, a s , of a very pure single crystal of Nb at low temperatures. We show that all the electronic attenuation is due to electrons with a BCS energy gap and find no evidence for either a very small or an anomalously large one.The normalized electronic attenuation a Jan is given in BCS theory by the well-known expression 2/(A), where/ is the Fermi function and A = A(T) is the temperature-dependent energy gap.The attenuation of longitudinal ultrasound along the [100] direction in Nb, resistivity ratio R m /R 0~5 200, has been measured with precision at low temperatures. The total attenuation in the normal state can be accurately deduced by a BCS calculation, with a single gap 2A(0) = (3.52±0.02)feT c , from the measured superconducting attenuation. No experimental evidence has been found for the existence of either a smaller or a larger gap. 764

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