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

  • Anil K. Bhatnagar
  • Belkis Gallardo


The enhanced conductivity σ of a thin superconducting film of thickness d ≪ ξ (T), the temperature-dependent coherence length, above its transition temperature T (but not too close to it) may be written as
$$\sigma ={{\sigma }_{AL}}+{{\sigma }_{M}}$$
where the contribution σ′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
$${{\sigma }_{AL}}/{{\sigma }_{N}}={{\tau }_{o}}/\tau $$
where τo = 1.52 ß 10−5R□, R□ =1/δNd,τ=(TT c )/T c , and δNis the normal-state conductivity. The second contribution σm’ was found by Maki2 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, Thompson3 introduced a low-momentum cutoff q c−1δ1/2,where
$$\sigma =\left( {{T}_{co}}-{{T}_{c}} \right)/{{T}_{C}}$$
is the relative shift of 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:
$${{\sigma }_{MT}}/{{\sigma }_{N}}=\left[ 2{{\tau }_{o}}/\left(\tau -\delta \right)\right]In\left(\tau /\delta \right)$$
with the constraint that (σMTN)≪δ,;δ≲0.1. The total excess conductivity normalized to δ Nis given by
$$\frac{\sigma }{{{\sigma }_{N}}}=\frac{\tau o}{\tau }+\frac{2{{\tau }_{o}}}{\tau -\delta }In\frac{\tau }{\delta }$$
When τ≪then σ′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


Cooper Pair Resistive Transition Parallel Magnetic Field Inverse Slope Excess Conductivity 
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    L.G. Aslamazov and A.I. Larkin, Soviet Phys.—Solid State 10, 875 (1968).Google Scholar
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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Anil K. Bhatnagar
    • 1
  • Belkis Gallardo
    • 1
  1. 1.Department of PhysicsSt. John’s UniversityJamaicaUSA

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