Low Temperature Physics-LT 13 pp 116-119 | Cite as

# Temperature Dependence of Ultrasonic Attenuation in the Mixed State of Pure Niobium

## Abstract

Experimental studies of the ultrasonic attenuation in the mixed state of intrinsic type II superconductors of moderate purity (Γ≃10^{3}) ^{1–3} showed that (∆α/α)^{ 2 } cc *H* _{ c2 }
— *H* or *T* _{ c } — *T*, somewhat as predicted.^{4} Here ∆α/α = (α_{n} - α)/α_{n} is the normalized change in attenuation from the normal state. More recently Cerdiera,^{5} Houghton,^{5,6} and Maki^{6} (hereafter CHM) have published a greatly revised theory taking into account the change in the electronic distribution near the transition. In this development there is thought to be a “BCS” regime, as has been reported,^{1–3} where the distribution function is essentially BCS-like and the attenuation can be described by α_{ s }
/α_{n} = 2/(1 + *e* ^{ ∆/kT }
) ∝ ∆(∆/*kT* ≪ 1), where ∆ = <(∆(r))^{2}>^{1/2} represents the space-averaged gap parameter. In addition to the BCS regime, a region closer to the transition is considered where the electronic distribution function no longer vanishes, but is greatly reduced at the Fermi surface. This gives rise to the description of this domain as “gapless” superconductivity. In this case the interaction depends on the density of electrons at the Fermi level and becomes similar to that in a dirty type II superconductor where the probability of electron-phonon scattering during the passage of an electron through a filament of normal-state metal is thought to be much greater than the corresponding probability during passage through a superconducting zone. Hence, we can expect ∆α ∝ area normal state ∝ magnetization ∝ ∆^{2} very close to the superconducting transition. The theory of CHM finds the transport coefficients determining the attenuation to have a simple dependence on the parameter *µ* = 2π^{
1/2}
(*∆/k* _{ c } *v* _{ F })^{ 2 } *k* _{ c } *1* at low temperatures. Here ∆ is the order parameter, *v* _{F} the Fermi velocity, l the electronic mean free path, and \(K_{c}^{2}\)
= *2πB/Ø* _{ 0 } is the reciprocal lattice vector of the flux line lattice. For our sample normal-state data^{7} show *l* ^{ −1 } \(\simeq \) \(l_{0}^{-1}\) +
*BT* ^{ 3 }, where *1* _{ 0 } = 40 x 10^{-3} cm and *B =* 1.2 cm^{−1} °K ^{−3}. In the BCS regime (∆α/α)^{2} ∝ ∆^{2}, while in the gapless regime ∆α/α ∝ *µ* ∝ ∆^{2}. For temperature drifts through the transition we can expand for small excursions ∆^{2} ∝ T_{ c } — *T*

## Keywords

Electronic Distribution Function Ultrasonic Attenuation Moderate Purity Pure Niobium Flux Line Lattice## Preview

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## References

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