Ultrasonic Studies of the Superconductivity of Doped Tin

Abstract

Detailed information concerning the anisotropy of the effective limiting superconducting energy gap A(0) of doped Sn has been obtained from measurements of the temperature dependence of the attenuation of compressional ultrasonic waves. Earlier results for the In-doped Sn system have been confirmed for other impurities, and analysis of the results has been made in terms of recent developments in the theory of dirty superconductivity. Measurements have been made for the sound-propagation vector q parallel to the [001], [110], and [100] directions in single crystals of In-, Cd-, Sb-, and Bi-doped Sn with impurity concentrations ranging from ^1 to 5 000 parts per million (ppm). The measured anisotropy between the [110] and [001] directions for pure Sn is ^20% of the average energy gap. It is found that this anisotropy is reduced to ~2% for values of the inverse resistivity ratio p >10"~2 and for AF C >15 mdegK. BCS theory, which was developed for isotropic, weak-coupling superconductors, is applicable to the most heavily doped samples; it is found that the energy gap (^1.76ksT c ) and the temperature dependence of ultrasonic attenuation are in agreement with the predictions of the theory. By comparing the energy-gap measurements from tunneling data with the energy gap obtained from ultrasonic-attenuation data, it is possible to demonstrate that the temperature dependence of the attenuation gives a measure of more than one energy gap. In addition to the gap obtained from the attenuation data at low temperatures, a larger gap can be observed near 2Y From tunneling data, the larger gap for q| [[001] is (1.9db0.05)foT , c ; the ultrasonic determination yields (1.92 ±0.02)ksT c . In addition, the temperature dependence of the larger gap is obtained near T c and is compared with BCS theory. For [1-T/rj ranging from ~4X10~2 to ^4X10^, it is found that the BCS-predicted approximation, A(r)/A(0) = 1.74[l~r/r c ] 1 / 2 , is accurate to ~2%.

Ultrasonic Studies of the Superconductivity of Doped Tin. II

“…The dependence of the £001] gap upon resistivity ratio in Cd-doped Sn is in precise agreement with the ultrasonic data. 4 The internal consistency between these results and the infrared-absorption data confirms that the change in anisotropy is indeed associated with the actual superconducting properties. There is some scatter between the thermal-conductivity data and ultrasonic data for the [11.0] direction; however, reduced anisotropy is indicated for the same values of resistivity ratio.…”

“…4 In order to avoid such extrapolation, Perz and Dobbs 1 extended their measurements to 0.8 °K, at which point the L. T. CLAIBORNE AND N. G. EINSPRUCH 166 attenuation was temperature-independent within the sensitivity of their apparatus. Their data were analyzed using this value as ao.…”

“…After the similarity to the results of Thomas was noted, the point was not discussed in detail in Ref. 4.…”

“…11 Attempts to use more sophisticated models to analyze data for Sn have been presented by the authors. 4 It is well established that small amounts of impurity added to a pure superconductor tend to reduce the transition temperature (cf. Lynton et al 12 ).…”

“…As was mentioned by the authors in Ref. 4, the [110] direction involves more complicated averaging for the ultrasonic wave than the [001], Hence it is not surprising that there may be some minor variations in the actual gap values for this direction compared with results obtained with other measurement techniques.…”