Dissipative superconducting state of non-equilibrium nanowires

Journal name:
Nature Physics
Volume:
10,
Pages:
567–571
Year published:
DOI:
doi:10.1038/nphys3008
Received
Accepted
Published online

The ability to carry electric current with zero dissipation is the hallmark of superconductivity1. This very property makes possible such applications ranging from magnetic resonance imaging machines to Large Hadron Collider magnets. But is it indeed the case that superconducting order is incompatible with dissipation? One notable exception, known as vortex flow, takes place in high magnetic fields2. Here we report the observation of dissipative superconductivity in far more basic configurations: superconducting nanowires with superconducting leads. We provide evidence that in such systems, normal current may flow in the presence of superconducting order throughout the wire. The phenomenon is attributed to the formation of a non-equilibrium state, where superconductivity coexists with dissipation, mediated by the so-called Andreev quasiparticles. Besides the promise for applications such as single-photon detectors3, the effect is a vivid example of a controllable non-equilibrium state of a quantum liquid. Thus our findings provide an accessible generic platform to investigate conceptual problems of out-of-equilibrium quantum systems.

At a glance

Figures

  1. Experimental observation of the voltage plateau.
    Figure 1: Experimental observation of the voltage plateau.

    a, The IV characteristics of sample A, at temperatures from 50 mK to 750 mK (right to left) at intervals of 50 mK. The voltage plateau with V0 ~ 52μV is visible between the bottom and top threshold currents Ib andIt. The inset shows a scanning electron microscope false colour image of the sample. Scale bar, 2μm. b, The temperature–current phase diagram, showing the voltage plateau existing at T 650mK. cf, IV characteristics of Zn samples A–C and Al sample D, respectively, measured at 450 mK with length, L, and normal-state resistance, Rn, as indicated. Sample A was measured in the well-filtered cryostat, whereas samples B–D were measured in the weakly filtered cryostat. The voltage axes are scaled to the Bardeen–Cooper–Schrieffer energy gap 2Δ0 = 3.52Tc for each sample. The voltage plateaux of all samples collapse onto V0/Δ0 ~ 0.43 ± 0.05, providing the evidence for the universality of the plateau state.

  2. The onset through bistability and the magnetic response of the voltage plateau.
    Figure 2: The onset through bistability and the magnetic response of the voltage plateau.

    a, The real-time evolution of the voltage for sample A held at a fixed current of 1.95μA and a temperature of 50 mK. The system undergoes stochastic switching between the superconducting and the voltage plateau states. b, Average lifetimes of the superconducting (τsc) and voltage plateau (τvp) states at elevated currents. The transition is accomplished by suppressing the superconducting state and stabilizing the voltage plateau state. c, Average lifetimes as functions of the perpendicular magnetic field. A magnetic field of only a few gauss suppresses the lifetime of the voltage plateau state by over two orders of magnitude. d, IV characteristics at magnetic fields from 0 to 18G in intervals of 2G. The bottom critical current (Ib) is seen to increase from 1.8μA to 2.5μA. e, Magnetic field–current phase diagram shows the high sensitivity of the voltage plateau to magnetic field. The plateau disappears at 19G.

  3. Dissipative superconducting state of the nanowire.
    Figure 3: Dissipative superconducting state of the nanowire.

    Top: Schematic of the system in which a superconducting nanowire is connected to superconducting leads. Bottom: The energy gap profile (solid brown) as a function of position along the system (horizontal direction). Phase slips occur in the centre of the wire (red region), generating non-equilibrium quasiparticles. At the two wire/lead interfaces they experience multiple Andreev reflections (shown schematically by blue–grey arrows) before escaping into the leads. This establishes a universal distribution, with the longitudinal part FL(ε) shown on the right. The self-consistency relation (2) results in the suppressed non-equilibrium gap 2Δ 0.34Δ0, dictating that a voltage eV0 = 2Δ should develop to maintain phase slip events.

References

  1. De Gennes, P. Superconductivity of Metals and Alloys 2nd edn (Westview Press, 1999).
  2. Blatter, G. et al. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 11251388 (1994).
  3. Goltsman, G. N. et al. Picosecond superconducting single-photon optical detector. Appl. Phys. Lett. 79, 705707 (2001).
  4. Eisaman, M. D., Fan, J., Migdall, A. & Polyakov, S. V. Invited Review Article: Single-photon sources and detectors. Rev. Sci. Instrum. 82, 071101 (2011).
  5. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 10311042 (2008).
  6. Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: An outlook. Science 339, 11691174 (2013).
  7. Wollman, D. A., Van Harlingen, D. J., Lee, W. C., Ginsberg, D. M. & Leggett, A. J. Experimental determination of the superconducting pairing state in YBCO from the phase coherence of YBCO-Pb dc SQUIDs. Phys. Rev. Lett. 71, 21342137 (1993).
  8. Tsuei, C. C. et al. Pairing symmetry and flux quantization in a tricrystal superconducting ring of Y Ba2Cu3O7−δ. Phys. Rev. Lett. 73, 593596 (1994).
  9. Mooij, J. E. & Nazarov, Y. V. Superconducting nanowires as quantum phase-slip junctions. Nature Phys. 2, 169172 (2006).
  10. Bezryadin, A. Superconductivity in Nanowires: Fabrication and Quantum Transport 1st edn (Wiley, 2012).
  11. Altomare, F. & Chang, A. M. One-Dimensional Superconductivity in Nanowires 1st edn (Wiley, 2013).
  12. Arutyunov, K. Yu, Golubev, D. S. & Zaikin, A. Superconductivity in one dimension. Phys. Rep. 464, 170 (2008).
  13. Sahu, M. et al. Individual topological tunnelling events of a quantum field probed through their macroscopic consequences. Nature Phys. 5, 503508 (2009).
  14. Shah, N., Pekker, D. & Goldbart, P. M. Inherent stochasticity of superconductor–resistor switching behavior in nanowires. Phys. Rev. Lett. 101, 207001 (2008).
  15. Li, P. et al. Switching currents limited by single phase slips in one-dimensional superconducting Al nanowires. Phys. Rev. Lett. 107, 137004 (2011).
  16. Singh, M. & Chan, M. H. W. Observation of individual macroscopic quantum tunneling events in superconducting nanowires. Phys. Rev. B 88, 064511 (2013).
  17. Stuivinga, M., Mooij, J. E. & Klapwijk, T. M. Current-induced relaxation of charge imbalance in superconducting phase-slip centers. J. Low Temp. Phys. 46, 555563 (1982).
  18. Skocpol, W., Beasley, M. R. & Tinkham, M. Phase-slip centers and nonequilibrium processes in superconducting tin microbridges. J. Low Temp. Phys. 16, 145167 (1974).
  19. Chen, Y., Snyder, S. D. & Goldman, A. M. Magnetic-field-induced superconducting state in Zn nanowires driven in the normal state by an electric current. Phys. Rev. Lett. 103, 127002 (2009).
  20. Chen, Y., Lin, Y-H., Snyder, S. D. & Goldman, A. M. Stabilization of superconductivity by magnetic field in out-of-equilibrium nanowires. Phys. Rev. B 83, 054505 (2011).
  21. Tian, M. et al. Suppression of superconductivity in zinc nanowires by bulk superconductors. Phys. Rev. Lett. 95, 076802 (2005).
  22. Tian, M., Kumar, N., Wang, J., Xu, S. & Chan, M. H. W. Influence of a bulk superconducting environment on the superconductivity of one-dimensional zinc nanowires. Phys. Rev. B 74, 014515 (2006).
  23. Tidecks, R. Current-Induced Nonequilibrium Phenomena in Quasi-One-Dimensional Superconductors 1st edn (Springer, 1990).
  24. Dinsmore, R. C. III, Bae, M-H. & Bezryadin, A. Fractional order Shapiro steps in superconducting nanowires. Appl. Phys. Lett. 93, 192505 (2008).
  25. Bae, M-H., Dinsmore, R. C. III, Sahu, M. & Bezryadin, A. Stochastic and deterministic phase slippage in quasi-one-dimensional superconducting nanowires exposed to microwaves. New J. Phys. 14, 043014 (2012).
  26. Barone, A. & Paterno, G. Physics and Applications of the Josephson Effect 1st edn (Wiley, 1982).
  27. Nagaev, K. E. Frequency-dependent shot noise in long disordered superconductornormal-metalsuperconductor contacts. Phys. Rev. Lett. 86, 3112 (2001).
  28. Usadel, K. D. Generalized diffusion equation for superconducting alloys. Phys. Rev. Lett. 25, 507510 (1970).
  29. Kamenev, A. Field Theory of Non-Equilibrium Systems (Cambridge Univ. Press, 2011).
  30. Vodolazov, D. Y. & Peeters, F. M. Enhancement of the retrapping current of superconducting microbridges of finite length. Phys. Rev. B 85, 024508 (2012).

Download references

Author information

Affiliations

  1. Department of Physics, University of California—Santa Barbara, Santa Barbara, California 93106, USA

    • Yu Chen
  2. School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA

    • Yu Chen,
    • Yen-Hsiang Lin,
    • Stephen D. Snyder,
    • Allen M. Goldman &
    • Alex Kamenev
  3. Department of Physics, University of Michigan-Ann Arbor, Ann Arbor, Michigan 48109, USA

    • Yen-Hsiang Lin
  4. William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA

    • Alex Kamenev
  5. Present address: Intel Corp., Portland, Oregon 97124, USA.

    • Stephen D. Snyder

Contributions

Y.C. and A.M.G. conceived and designed the experiment. Y.C. and S.D.S. fabricated the devices. Y.C and Y-H.L. performed the measurements. A.K. provided theoretical analysis and co-wrote the manuscript with Y.C. and A.M.G. All authors contributed to the discussion and presentation of the results.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (508KB)

    Supplementary Information

Additional data