Aslamazov-Larkin Research Articles

Two-dimensional paraconductivity in superconducting Bi1.6Pb0.4Sr2Ca2Cu3OY

Measurements of the electrical resistance R of polycrystalline samples of Bi1.6Pb0.4Sr2Ca2Cu3OY with the 108-K superconducting phase show that the Aslamazov–Larkin (AL) two-dimensional paraconductivity corrections are observable in the vicinity of the mean-field theory transition temperatureT0C. The effective thickness, d≊23 Å, of the superconducting electronic sheet as found from the zero field data is comparable to the a,b-plane separation. This result agrees well with the recent single-crystal data. The data for magnetic fields up to 1.5 T also show paraconductivity effects. T0C (H) is found to decrease as a function of increasing magnetic field H; this result agrees with the prediction of the AL model.

Excess conductivity in Tl 1Ca 3Ba 1Cu 3O χ and Bi 1Ca 1Sr 1Cu 2O χ systems due to thermodynamic fluctuations

The excess conductivity (Δσ) in Tl 1Ca 3Ba 1Cu 3O χ and Bi 1Ca 3Sr 1Cu 2O χ (nominal compositions) is determined using the linear extrapolation method and Anderson-Zou formula. Δσ for the TI-system shows a 2-dimensional character and is well described by the Aslamazov-Larkin (A-L) contribution for a layered superconductor. The interlayer coupling for the TI-system is found to be very small. The excess conductivity in a magnetic field perpendicular to the current direction Δσ⊥( H), for T≤ T c and H≥62; H c2 shows a 3-dimensional character. Similar behavior is also observed in the Bi-system.

Excess electrical conductivity above Tcin high-temperature superconductors, and thermal fluctuations

The excess electrical conductivity, Delta sigma , above Tc in single-phase (within 4%) Ba2LnCu3O7- delta compounds, with Ln=Y, Ho and Sm, has been measured in the reduced temperature range 5*10-4<or approximately= epsilon <or approximately=1; this extends previous results almost one order of magnitude closer to Tc. This allows the authors to observe, for the first time, four different Delta sigma ( epsilon ) regions, with different critical exponents. These regions are analysed in terms of the Aslamazov-Larkin (AL) theory for thermal fluctuations in BCS superconductors and also using some dynamical scaling ideas. The results suggest that the Ginzburg-Landau mean-field region is located in the high-temperature range. In that case, the corresponding critical exponent is of the order of -1/2, in agreement with 3D AL superconductivity, although the strong intrinsic anisotropy, the polycrystallinity and the local defects of the samples may cause the disagreement with the AL model observed for the amplitude of the fluctuation effects.

Probing thermodynamic fluctuations in high temperature superconductors

We probe thermodynamic fluctuations in HTSC by measuring the excess electrical conductivity, Δσ, abovr T c in single-phase (within 4%) Ba 2LnCu 3O 7−δ compounds, with LnY, Ho and Sm. As expected, the measured relative effect, Δσ / σ (300 K), is much more important in HTSC than for low-temperature superconductors (at least one order of magnitude). In the reduced temperature region −5< ln ϵ ≡ ln [ (T-T c)/T c] <−2, Δσ may be written as Δσ/ σ ( 300 K ) = Aϵ x, where A is a temperature-independent amplitude. x is found to be similar for all compounds, with average value <x>=−0.47 ± 0.06. This result confirms an universal critical behaviour of Δσ in HTSC, and the value of <x> agrees with that predicted by the Aslamazov-Larkin (AL) theory for three-dimensional BCS superconductivity. However, A shows a normal conductivity dependence which is not accounted for by the AL theory.

Quantum corrections to the resistance in two-dimensional disordered superconductors aboveTc: Al, Sn, and amorphousBi0.9Tl0.1films

Disordered films of superconductors above their transition temperature ${T}_{c}$ show several quantum corrections to the conductance, weak localization (WL), two contributions from the retarded Coulomb interaction, and two contributions from superconducting fluctuations, the Aslamazov-Larkin (AL) and the Maki-Thompson (MT) terms. In a magnetic field, most of them show a magnetoresistance and all are temperature dependent. In this paper the temperature and field dependence of the resistance is measured for Al, Sn, and amorphous ${\mathrm{Bi}}_{0.9}$${\mathrm{Tl}}_{0.1}$ films. This covers the weak-coupling and the extremely-strong-coupling superconductors as well. Of particular interest are the AL and the MT terms. The latter can be reduced by a pair-breaking mechanism. This pair breaking is caused by the inelastic-scattering time of the conduction electrons and can be measured by weak localization. Al has only a small spin-orbit scattering but by covering it with \textonequarter{} atomic layer of Au it can be transformed into a strong spin-orbit scatterer. This allows an independent determination of the inelastic lifetime ${\ensuremath{\tau}}_{i}$ and spin-orbit scattering time ${\ensuremath{\tau}}_{\mathrm{s}.\mathrm{o}.}$ and therefore a complete examination of the theory and its consistency. The agreement between experiment and theory is very good for the magnetoresistance. However, the theory for the temperature dependence of the resistance fails (with the exception of the contribution of WL). For the intermediate- and strong-coupling superconductors the applicability of the existing theories is restricted. The magnetoresistance of amorphous ${\mathrm{Bi}}_{0.9}$${\mathrm{Tl}}_{0.1}$ is essentially determined by the AL contribution.

Fluctuation-Induced Conductivity above the Superconducting Transition Temperature in Indium Films Containing Gadolinium Impurities

Fluctuation-induced conductivity (FIC) in indium films containing paramagnetic impurities (gadolinium) is investigated. The FIC is well described as the sum of the Aslamazov-Larkin (AL) term, the Maki-Thompson (MT) term and the third term. The sum of the AL term and the MT term is insufficient to express the FIC. The pair-breaking parameter δ depends not only on the normal state sheet resistance but also on the concentration of gadolinium impurities in the manner predicted by Thompson. Experimental data are analysed also by the use of the formulae proposed by one of the present authors (K.O) in which the magnetic impurity effect is explicitly taken into account.

Supercooling magnetic field and thermodynamic fluctuations in very thin superconducting aluminum films

We have used the fluctuation conductivity of very thin superconducting aluminum films in parallel magnetic fields $H&gt;{H}_{c}(T)$ to determine the supercooling field associated with Pauli paramagnetism at low temperature. Fields up to 9 T and temperatures down to 0.4 K were employed. The supercooling field was compared with theory and values of the spin-orbit scattering rate $b$ and orbital Maki parameter $c$ were obtained. The width of the superconducting transitions was compared with the Aslamazov-Larkin (AL) and Maki-Thompson (MT) contributions to the fluctuation conductivity as extended by Aoi to the Pauli paramagnetic limit. In general, the transitions were wider than expected from the AL contribution alone, but narrower than expected from the sum of the AL and MT contributions.

Effects of Magnetic Impurities on Paraconductivity in Superconductors

Fluctuation-induced conductivity above T c in superconductors containing magnetic impurities is calculated within the context of the Abrikosov-Gor'kov theory. Excess conductivity is expressed as the sum of the Aslamazov-Larkin (AL)term, the Maki-Thompson (MT) term and the third term. The third term has no critical singularity in a bulk. The critical behavior of the AL term and that of the MT term are similar to those in the absence of magnetic impurities, respectively. But the coefficients of these terms as well as the reduced temperature are renormalized owing to the presence of magnetic impurities. The Thompson parameter δ is derived from the calculation and is expressed as a function of temperature and the spin-flip relaxation time. The third term in a film is less strongly divergent but it is important at higher temperatures.

Fluctuation-Induced Conductivity above the Superconducting Transition Temperature in Thallium Films

Excess conductivity due to fluctuations above the superconducting transition temperature T c in two-dimensional systems is studied both theoretically and experimentally. Theoretically a small correction term added to the Maki-Thompson (MT) term is proposed. This correction term becomes not less important at relatively high temperatures. Experimental results on thallium films are as follows: (1) In the zero electric field limit excess conductivity is well described as the sum of the Aslamazov-Larkin (AL) and MT terms when T is close to T c . However at relatively high temperatures, \(\eta{\gtrsim}0.1\) (η=ln ( T / T c )), the contribution from the above-mentioned correction term is observed. (2) An empirical relation between the pair-breaking parameter δ and R N sq was found to be δ=δ 0 + const × R N sq . (3) When η is small excess conductivity in finite electric field is well expressed as the sum of the nonlinear AL and MT terms. (4) The characteristic electric field is observed to be proportional to η 3/2 .

Fluctuations and the resistive transition in paramagnetically limited superconductors

We have studied, both theoretically and experimentally, the extra conductivity ${\ensuremath{\sigma}}_{\mathrm{fl}}$ due to thermal fluctuations in high-field superconductors in the Pauli-paramagnetic limit (SPPL). We first investigate theoretically the Aslamazov-Larkin (AL) term, and show that the Pauli-paramagnetic effect in the AL term can be included by renormalizing the thickness of the film. Then we calculate the pair-breaking function for the Maki-Thompson (MT) term in a magnetic field within the lowest-order approximation of Keller and Korenman and show that in contrast to ordinary superconductors the MT term in SPPL can be enhanced by a weak parallel field. We also report the first experimental measurements of ${\ensuremath{\sigma}}_{\mathrm{fl}}$ in SPPL. The angular dependence of the AL term is found to be essentially in agreement with the calculation of Aoi reported earlier. Near ${T}_{c0}$ the MT term is observed to be suppressed by a parallel field. We also study the effect of a perpendicular field, and find, both theoretically and experimentally, that in SPPL the MT term appears to be suppressed by a perpendicular field.

Angular dependence of the resistive transitions in superconducting films in a magnetic field

The resistive transitions aboveH c on Al films with the thicknessd<ξ(0) have been measured as a function of the angle ϑ between the film surface and the magnetic field, where ξ(0) is the coherence length at 0 K. An observed broadness in the transitions is considered to be due to fluctuations aboveH c and is compared with Aoi's theories taking into account the Aslamazov—Larkin (AL) contribution only, or both the AL and an anomalous (Maki) contribution. At all angles the observed electrical conductivity due to fluctuations σ' is larger than the theoretical predictions based on the AL contribution alone. Except for angles near ϑ=0, the observed σ' can be explained by adding the anomalous contribution to that of AL.