Low Temperature Physics-LT 13 pp 654-658 | Cite as

# A Study of Fluctuation Effects on Resistive Transition to Superconductivity in Thin Indium Films

Chapter

## Abstract

The enhanced conductivity σ of a thin superconducting film of thickness where the contribution σ′ where τ is the relative shift of with the constraint that (σWhen τ≪then σ′

*d*≪ ξ (T), the temperature-dependent coherence length, above its transition temperature T (but not too close to it) may be written as$$\sigma ={{\sigma }_{AL}}+{{\sigma }_{M}}$$

(1)

_{AL}comes from the formation of short-lived Cooper pairs above*T*_{ c }and was first considered theoretically by Aslamazov and Larkin.^{1}They showed that$${{\sigma }_{AL}}/{{\sigma }_{N}}={{\tau }_{o}}/\tau $$

(2)

_{o}= 1.52 ß 10^{−5}R□, R□ =1/δ_{N}d,τ=(*T*−*T*_{ c })/*T*_{ c }, and δ_{N}is the normal-state conductivity. The second contribution σ_{m}’ was found by Maki^{2}and comes from the interaction of normal electrons with Cooper pairs. This term was found to be divergent for thin films.^{3}In order to remove this divergence, Thompson^{3}introduced a low-momentum cutoff q_{ c}=ξ^{−1}δ^{1/2},where$$\sigma =\left( {{T}_{co}}-{{T}_{c}} \right)/{{T}_{C}}$$

(3)

*T*_{ c }from some original value*T*_{ c0}due to a pair-breaking interaction. Thompson’s procedure leads to the following expression for σ′_{M}:$${{\sigma }_{MT}}/{{\sigma }_{N}}=\left[ 2{{\tau }_{o}}/\left(\tau -\delta \right)\right]In\left(\tau /\delta \right)$$

(4)

_{MT}/δ_{N})≪δ,;δ≲0.1. The total excess conductivity normalized to δ_{N}is given by$$\frac{\sigma }{{{\sigma }_{N}}}=\frac{\tau o}{\tau }+\frac{2{{\tau }_{o}}}{\tau -\delta }In\frac{\tau }{\delta }$$

(5)

_{MT}beomes negligible and σ is given by only the AL term; however, far from the transition Eq. (5) leads to a larger transition width than predicted by the AL theory. This has indeed been observed in aluminum, tin, and lead films’; however, the AL width was found in the case of amorphous bismuth, lead, and gallium films.^{5}## Keywords

Cooper Pair Resistive Transition Parallel Magnetic Field Inverse Slope Excess Conductivity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

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- 4.J.E. Crow, A.K. Bhatnagar, and T. Mihalisin,
*Phys. Rev. Lett*.**28**25 (1971), and references therein.Google Scholar - 5.
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## Copyright information

© Springer Science+Business Media New York 1974