Large oscillations of the magnetoresistance in nanopatterned high-temperature superconducting films

Journal name:
Nature Nanotechnology
Year published:
Published online


Measurements on nanoscale structures constructed from high-temperature superconductors are expected to shed light on the origin of superconductivity in these materials1, 2, 3, 4, 5, 6, 7. To date, loops made from these compounds have had sizes of the order of hundreds of nanometres8–11. Here, we report the results of measurements on loops of La1.84Sr0.16CuO4, a high-temperature superconductor that loses its resistance to electric currents when cooled below ~38 K, with dimensions down to tens of nanometres. We observe oscillations in the resistance of the loops as a function of the magnetic flux through the loops. The oscillations have a period of h/2e, and their amplitude is much larger than the amplitude of the resistance oscillations expected from the Little–Parks effect12, 13. Moreover, unlike Little–Parks oscillations, which are caused by periodic changes in the superconducting transition temperature, the oscillations we observe are caused by periodic changes in the interaction between thermally excited moving vortices and the oscillating persistent current induced in the loops. However, despite the enhanced amplitude of these oscillations, we have not detected oscillations with a period of h/e, as recently predicted for nanoscale loops of superconductors with d-wave symmetry1, 2, 3, 4, 5, 6, or with a period of h/4e, as predicted for superconductors that exhibit stripes7.

At a glance


  1. Patterned superconducting film.
    Figure 1: Patterned superconducting film.

    Main panel: scanning electron microscope (SEM) image of a La1.84Sr0.16CuO4 superconducting film covered with a patterned layer of poly(methyl methacrylate) (PMMA) resist (thin lines with bright edges). The left inset shows an SEM image of a part of the resulting superconducting network (150 × 150-nm2 loops separated by 500 × 500-nm2 loops) after the uncovered parts of the film were removed by ion milling. The right inset shows the measured (white circles) temperature dependence of the network (30 × 30 µm2) resistance in zero magnetic field near the superconducting transition; the current is 1 µA. In the patterned film the onset temperature for superconductivity is 30.2 K and the transition width is ~2 K (compared with 38 K and ~0.5 K for the as-grown film).

  2. Magnetoresistance oscillations.
    Figure 2: Magnetoresistance oscillations.

    Resistance of the La1.84Sr0.16CuO4 network shown in Fig. 1 as a function of applied magnetic field, measured at 28.4 K. The oscillations are superimposed on a parabolic-like background. The amplitude of the oscillations, ΔR, is well defined at low fields. Inset: ΔR as a function of temperature; the solid line is a theoretical fit based on equation (5). The dashed line is an upper limit for the amplitude of resistance oscillations calculated for the Little–Parks effect (right axis; note that the scale on this axis is expanded tenfold).

  3. Comparison of measured and calculated magnetoresitance oscillations.
    Figure 3: Comparison of measured and calculated magnetoresitance oscillations.

    a, Measured normalized resistance of the network shown in Fig. 1 as a function of the applied magnetic field and temperature. b, Normalized resistance calculated using equation (4) for wire width w = 25 nm, film thickness d = 26 nm, zero-temperature penetration depth λ0 = 750 nm and coherence length ξ0 = 2.4 nm. The calculation was made for circular loops of the same area as the square loops: that is, with an effective radius = a/π = 83.5 nm (a = 150 nm is the actual loop side length). The values for λ0 and ξ0 are obtained from the fit of equation (5) to the temperature dependence of the amplitude shown in the inset to Fig. 2. The colour changes from blue to green to orange to white as the resistance increases from zero to the normal-state value.

  4. Periodicity of the magnetoresistance oscillations.
    Figure 4: Periodicity of the magnetoresistance oscillations.

    a,b, Amplitude of the Fourier transform of the magnetoresistance oscillations versus inverse magnetic flux in the 150-nm loops at 28.5 K (a) and the 75-nm loops at 28 K (b). The h/2e periodicity is apparent, but the h/e periodicity is absent, and the h/4e periodicity appears as the second harmonic of the h/2e fundamental component.


  1. Barash, Y. S. Low-energy subgap states and the magnetic flux periodicity in d-wave superconducting rings. Phys. Rev. Lett. 100, 177003 (2008).
  2. Juricic, V., Herbut, I. F. & Tesanovic, Z. Restoration of the magnetic hc/e-periodicity in unconventional superconductors. Phys. Rev. Lett. 100, 187006 (2008).
  3. Loder, F. et al. Magnetic flux periodicity of h/e in superconducting loops. Nature Phys. 4, 112115 (2008).
  4. Vakaryuk, V. Universal mechanism for breaking the hc/2e periodicity of flux-induced oscillations in small superconducting rings. Phys. Rev. Lett. 101, 167002 (2008).
  5. Wei, T.-C. & Goldbart, P. M. Emergence of h/e-period oscillations in the critical temperature of small superconducting rings threaded by magnetic flux. Phys. Rev. B 77, 224512 (2008).
  6. Zhu, J.-X. & Quan, H. T. Magnetic flux periodicity in a hollow d-wave superconducting cylinder. Phys. Rev. B 81, 054521 (2010).
  7. Berg, E., Fradkin, E. & Kivelson, S. A. Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors. Nature Phys. 5, 830833 (2009).
  8. Gammel, P. L., Polakos, P. A., Rice, C. E., Harriott, L. R. & Bishop, D. J. Little–Parks oscillations of T c in patterned microstructures of the oxide superconductor YBa2Cu3O7: experimental limits on fractional-statistics-particle theories. Phys. Rev. B 41, 25932596 (1990).
  9. Castellanos, A., Wordenweber, R., Ockenfuss, G., Hart, A. v. d. & Keck, K. Preparation of regular arrays of antidots in YBa2Cu3O7 thin films and observation of vortex lattice matching effects. Appl. Phys. Lett. 71, 962964 (1997).
  10. Crisan, A. et al. Anisotropic vortex channeling in YBa2Cu3O7+δ thin films with ordered antidot arrays. Phys. Rev. B 71, 144504 (2005).
  11. Ooi, S., Mochiku, T., Yu, S., Sadki, E. S. & Hirata, K. Matching effect of vortex lattice in Bi2Sr2CaCu2O8+y with artificial periodic defects. Physica C 426–431, 113117 (2005).
  12. Little, W. A. & Parks, R. D. Observation of quantum periodicity in the transition temperature of a superconducting cylinder. Phys. Rev. Lett. 9, 912 (1962).
  13. Parks, R. D. & Little, W. A. Fluxoid quantization in a multiply-connected superconductor. Phys. Rev. A 133, 97103 (1964).
  14. Mooij, J. E. & Schön, G. B. J. (eds) Proc. NATO Workshop on Coherence in Superconducting Networks. Physica. B 152, 1302 (1988).
  15. Tinkham, M. Consequences of fluxoid quantization in the transitions of superconducting films. Rev. Mod. Phys. 36, 268276 (1964).
  16. Tinkham, M. Introduction to Superconductivity (McGraw-Hill, 1996).
  17. Koshnick, N. C., Bluhm, H., Huber, M. E. & Moler, K. A. Fluctuation superconductivity in mesoscopic aluminum rings. Science 318, 14401443 (2007).
  18. Wen, H. H. et al. Hole doping dependence of the coherence length in La2+xSrxCuO4 thin films. Europhys. Lett. 64, 790796 (2003).
  19. Yeshurun, Y., Malozemoff, A. P. & Shaulov, A. Magnetic relaxation in high-temperature superconductors. Rev. Mod. Phys. 68, 911949 (1996).
  20. Tinkham, M. Resistive transition of high-temperature superconductors. Phys. Rev. Lett. 61, 16581661 (1988).
  21. Blatter, G., Feigel'man, M. V., Geshkenbein, V. B., Larkin, A. I. & Vinokur, V. M. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 11251388 (1994).
  22. London, F. On the problem of the molecular theory of superconductivity. Phys. Rev. 74, 562573 (1948).
  23. Kirtley, J. R. et al. Fluxoid dynamics in superconducting thin film rings. Phys. Rev. B 68, 214505 (2003).
  24. Kogan, V. G., Clem, J. R. & Mints, R. G. Properties of mesoscopic superconducting thin-film rings: London approach. Phys. Rev. B 69, 064516 (2004).
  25. Pearl, J. Current distribution in superconducting films carrying quantized fluxoids. Appl. Phys. Lett. 5, 6566 (1964).
  26. Qiu, C. & Qian, T. Numerical study of the phase slip in two-dimensional superconducting strips. Phys. Rev. B 77, 174517 (2008).
  27. Yeshurun, Y. & Malozemoff, A. P. Giant flux creep and irreversibility in an Y-Ba-Cu-O crystal: an alternative to the superconducting-glass model. Phys. Rev. Lett. 60, 22022205 (1988).
  28. Hopkins, D. S., Pekker, D., Goldbart, P. M. & Bezryadin, A. Quantum interference device made by DNA templating of superconducting nanowires. Science 308, 17621765 (2005).
  29. Pekker, D., Bezryadin, A., Hopkins, D. S. & Goldbart, P. M. Operation of a superconducting nanowire quantum interference device with mesoscopic leads. Phys. Rev. B 72, 104517 (2005).
  30. Hoole, A. C. F., Welland, M. E. & Broers, A. N. Negative PMMA as a high-resolution resist—the limits and possibilities. Semicond. Sci. Technol. 12, 11661170 (1997).

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  1. Department of Physics, Institute of Superconductivity and Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel

    • Ilya Sochnikov,
    • Avner Shaulov &
    • Yosef Yeshurun
  2. Brookhaven National Laboratory, Upton, New York 11973-5000, USA

    • Gennady Logvenov &
    • Ivan Božović


G.L and I.B. synthesized and characterized the superconducting films. I.S. designed and made the patterns, performed the magnetoresistance measurements and analysed the data. All authors contributed to the theoretical interpretation and were involved in the completion of the manuscript.

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