Fluctuation Superconductivity in Mesoscopic Aluminum Rings

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Science  30 Nov 2007:
Vol. 318, Issue 5855, pp. 1440-1443
DOI: 10.1126/science.1148758

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  1. Fig. 1.

    (A) Diagram of the direct current SQUID susceptometer. One field coil applies up to 50 Gauss of field to the sample, whose response couples a magnetic flux into the 4-μm pickup loop. A second counter-wound (C-W) loop cancels the SQUID's response to the applied field to within one part in 104. Additional modulation coils maintain the optimum working point. (B) The SQUID's pickup loop (white) and field coil (blue) are positioned over a single micrometer-scale aluminum ring. In situ background measurements allow the magnetic flux induced by currents in the ring to be unambiguously distinguished from the applied field, which is up to seven orders of magnitude larger.

  2. Fig. 2.

    SQUID signal (left axis) and ring current (right axis) as a function of applied flux Φa for two rings, both with d = 60 nm and w = 110 nm. The fluctuation theory (dashed red) was fit to the data (blue) through the temperature analysis shown in Fig. 3. (A to C) R = 0.35 μm, fitted Tca=0) = 1.247 K, and γ = 0.075. The green line is the theoretical mean field response for T = 1.22 K and shows the characteristic Little-Parks line shape, in which the ring is not superconducting near Φa = Φ0/2. The excess persistent current in this region indicates the large fluctuations in the Little-Parks regime. (D) R = 2 μm, fitted Tca=0) = 1.252 K, and γ = 13. The periodic response (right inset) shows 1D treatment is appropriate and can be approximated by a thermal average over mean field G-L fluxoid states (Eq. 1 and SOM text) until additional fluctuations contribute near Tc.

  3. Fig. 3.

    Susceptibility data (symbols) and fits (lines) at Φa = 0 (positive values) and Φ0/2 (negative values) for 110-nm-wide 60-nm-thick rings with various values of R. (A) Smaller rings have a larger temperature region where the Little-Parks criterion χ(T)>2R is satisfied and thus have a larger region with a reduced Φa = Φ0/2 response. (B) Φa = 0 susceptibility scaled with the cross section and radius to show the effective mean field superfluid density around Tc. Smaller rings have an enhanced fluctuation response. (C) When the temperature is scaled by the correlation energy, Ec, the susceptibility is uniquely determined by the size parameter γ. The gray and green shaded regions indicate the temperature above Tca) when Φ = 0 and Φ0/2, respectively. The fluctuation response above Tca) is enhanced for Φa = Φ0/2. The dotted line shows a Gaussian prediction (SOM text) that is valid at some γ-dependent temperature above Tca). When γ ≳ 1, the response at Φa = 0 and the response at Φa = Φ0/2 are comparable in the Little-Parks regime, which corresponds to a fluctuation-dominated sinusoidal I–Φa response.

  4. Fig. 4.

    Mean field theory (green), fluctuation theory (dashed red), and data (blue) for three rings with different γ parameters. The mean field response is derived from the fluctuation theory parameters for each ring at the given temperature. (A) T = 1.20 K. In small γ rings, the Little-Parks line shape is clearly observable. (B) T = 1.25 K. When γ ≈ 1, the reduction of the response due to the Little-Parks effect is significantly suppressed. (C) T = 1.25 K. In large γ rings, the Little-Parks effect is completely washed out by fluctuations, which affect the responses at all flux values.

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