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## Preview

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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