Transport through Andreev bound states in a graphene quantum dot

Journal name:
Nature Physics
Volume:
7,
Pages:
386–390
Year published:
DOI:
doi:10.1038/nphys1911
Received
Accepted
Published online

When a low-energy electron is incident on an interface between a metal and superconductor, it causes the injection of a Cooper pair into the superconductor and the generation of a hole that reflects back into the metal—a process known as Andreev reflection. In confined geometries, this process can give rise to discrete Andreev bound states (ABS), which can enable transport of supercurrents through non-superconducting materials and have recently been proposed as a means of realizing solid-state qubits1, 2, 3. Here, we report transport measurements of sharp, gate-tunable ABS formed in a superconductor–quantum dot (QD)–normal system realized on an exfoliated graphene sheet. The QD is formed in graphene beneath a superconducting contact as a result of a work-function mismatch4, 5. Individual ABS form when the discrete QD levels are proximity-coupled to the superconducting contact. Owing to the low density of states of graphene and the sensitivity of the QD levels to an applied gate voltage, the ABS spectra are narrow and can be continuously tuned down to zero energy by the gate voltage.

At a glance

Figures

  1. Configuration and doping characteristics of the graphene device.
    Figure 1: Configuration and doping characteristics of the graphene device.

    a, Scanning electron micrograph of a device with an overlaid measurement circuit. Graphene is false coloured orange, large end contacts are Cr/Au and middle tunnel probes are Pb/In. The scale bar is 5μm. b, Above: side-view schematic diagram of the device. Below: Illustration of the doping profile as a function of position along the device (blue line) and Dirac cones showing the location of the Fermi level. The square well under the tunnel probe shows where p–n junctions create a confining potential for the quantum dot. c, End-to-end conductance versus back-gate for sample A (single layer), showing the Dirac cone. d, End-to-end conductance versus back-gate for sample B (multilayer). The asymmetry in c and d shows that the bulk graphene is p-doped by the back-gate.

  2. Schematic diagrams of the graphene-QD-SC device.
    Figure 2: Schematic diagrams of the graphene–QD–SC device.

    a, Schematic diagram of the QD formed in graphene by a work-function mismatch at the Pb interface. b, Schematic energy-level diagram of the graphene–QD–SC system. The density of states of the p-type graphene and SC tunnel probe is shown on the left and right, respectively, with filled states indicated. The AlOx tunnel barrier is indicated in green on the right and the p–n junction is indicated in light blue on the left. Blue/red energy levels refer to Andreev bound states. The solid (dashed) lines represent states that have dominant particle (hole) character. The bias voltage, Vb, is shown tuned to enable resonant subgap conduction.

  3. Superconducting tunnelling data showing oscillations and subgap ABS peaks.
    Figure 3: Superconducting tunnelling data showing oscillations and subgap ABS peaks.

    a, Tunnelling differential conductance versus bias voltage (set-up as in Fig. 1a), for the multilayer graphene (sample B). Large conductance oscillations outside the gap are probably Fabry–Perot-like interference effects. Similar oscillations and subgap peaks are seen in sample A. Two ABS peaks are visible inside the SC gap. b, Temperature dependence of the subgap peaks. The temperature from the widest SC gap is 0.26, 0.45, 0.67, 0.86, 1.25 and 1.54K. The peaks decrease in amplitude and increase in breadth as temperature is increased to ~0.8K, then remain constant; this is consistent with a crossover from a quantum to a classical dot regime.

  4. Back-gate dependence of Andreev bound states.
    Figure 4: Back-gate dependence of Andreev bound states.

    a, Two-dimensional map of tunnelling differential conductance versus back-gate voltage (x axis) and bias voltage (y axis) on a log scale for the single-layer device (sample A). Bright white lines inside the gap (marked as 2Δ) are subgap peaks, or ABS, which are symmetric about zero bias and gate dependent. b, A fit of the conductance data from the detailed transport calculations for a quantum dot with two levels, a finite charging energy and couplings to normal-metal and superconducting leads (see main text and Supplementary Discussion, part I).

  5. Diagrams showing the energy dependence of Andreev bound states.
    Figure 5: Diagrams showing the energy dependence of Andreev bound states.

    Left: Energy diagram showing the evolution of ABS levels in a quantum dot with varying gate voltage. U is the charging energy of the quantum dot and Δ is the superconducting gap of the tunnel probe. Right: Three resonant tunnelling diagrams corresponding to the three different gate voltages marked on the left-hand diagram. The solid (dashed) lines represent states which have dominant particle (hole) character. The bias voltages required for conductance through the ABS are the energy differences between the bound-state levels and EF of the SC. For point 1, one Andreev bound state (red) is below the SC gap edge and one (blue) is above; this gives two subgap peaks (red levels) in the conductance at finite (positive and negative) bias voltage. At point 2, an ABS is tuned to zero energy, which leads to a zero-bias conductance peak. At point 3, the ABS level is at the gap edge, which leads to subgap peaks that are pushed towards the gap edge.

References

  1. Shafranjuk, S. E., Nevirkovets, I. P. & Ketterson, J. B. A qubit device based on manipulations of Andreev bound states in double-barrier Josephson junctions. Solid State Commun. 121, 457460 (2002).
  2. Zazunov, A., Shumeiko, V. S., Bratus’, E. N., Lantz, J. & Wendin, G. Andreev level qubit. Phys. Rev. Lett. 90, 087003 (2003).
  3. Zazunov, A., Shumeiko, V. S., Wendin, G. & Bratus’, E. N. Dynamics and phonon-induced decoherence of Andreev level qubit. Phys. Rev. B 71, 214505 (2005).
  4. Giovannetti, G. et al. Doping graphene with metal contacts. Phys. Rev. Lett. 101, 026803 (2008).
  5. Huard, B., Stander, N., Sulpizio, J. A. & Goldhaber-Gordon, D. Evidence of the role of contacts on the observed electron–hole asymmetry in graphene. Phys. Rev. B 78, 121402 (2008).
  6. Deutscher, G. Andreev–Saint-James reflections: A probe of cuprate superconductors. Rev. Mod. Phys. 77, 109135 (2005).
  7. Heersche, H. B., Jarillo-Herrero, P., Oostinga, J. B., Vandersypen, L. M. K. & Morpurgo, A. F. Induced superconductivity in graphene. Solid State Commun. 143, 7276 (2007).
  8. Ojeda-Aristizabal, C., Ferrier, M., Gueron, S. & Bouchiat, H. Tuning the proximity effect in a superconductor–graphene–superconductor junction. Phys. Rev. B 79, 165436 (2009).
  9. Du, X., Skachko, I. & Andrei, E. Y. Josephson current and multiple Andreev reflections in graphene SNS junctions. Phys. Rev. B 77, 184507 (2008).
  10. Beenakker, C. W. J. Specular Andreev reflection in graphene. Phys. Rev. Lett. 97, 067007 (2006).
  11. Meng, T., Florens, S. & Simon, P. Self-consistent description of Andreev bound states in Josephson quantum dot devices. Phys. Rev. B 79, 224521 (2009).
  12. Sköldberg, J., Löfwander, T., Shumeiko, V.S. & Fogelström, M. Spectrum of Andreev bound states in a molecule embedded inside a microwave-excited superconducting junction. Phys. Rev. Lett. 101, 087002 (2008).
  13. Zhang, Z.Y. Differential conductance through a NINS junction on graphene. J. Phys. Condens. Matter 20, 445220 (2008).
  14. Ossipov, A., Titov, M. & Beenakker, C. W. J. Reentrance effect in a graphene n–p–n junction coupled to a superconductor. Phys. Rev. B 75, 241401 (2007).
  15. Deacon, R. S. et al. Tunneling spectroscopy of Andreev energy levels in a quantum dot coupled to a superconductor. Phys. Rev. Lett. 104, 076805.
  16. Eichler, A. et al. Even–odd effect in Andreev transport through a carbon nanotube quantum dot. Phys. Rev. Lett. 99, 126602 (2007).
  17. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183191 (2007).
  18. Chen, Y. F., Dirks, T., Al-Zoubi, G., Birge, N. O. & Mason, N. Nonequilibrium tunneling spectroscopy in carbon nanotubes. Phys. Rev. Lett. 102, 036804 (2009).
  19. Dirks, T., Chen, Y. F., Birge, N. O. & Mason, N. Superconducting tunnelling spectroscopy of a carbon nanotube quantum dot. Appl. Phys. Lett. 95, 192103 (2009).
  20. Park, J. & McEuen, P. L. Formation of a p-type quantum dot at the end of an n-type carbon nanotube. Appl. Phys. Lett. 79, 13631365 (2001).
  21. Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nature Phys. 5, 222226 (2009).
  22. Shytov, A. V., Rudner, M. S. & Levitov, L. S. Klein backscattering and Fabry–Perot interference in graphene heterojunctions. Phys. Rev. Lett. 101, 156804 (2008).
  23. Silvestrov, P. G. & Efetov, K. B. Quantum dots in graphene. Phys. Rev. Lett. 98, 016802 (2007).
  24. Pillet, J-D. et al. Andreev bound states in a supercurrent-carrying carbon nanotube revealed. Nature Phys. 6, 965969 (2010).
  25. Blonder, G. E., Tinkham, M. & Klapwijk, T. M. Transition from metallic to tunnelling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion. Phys. Rev. B 25, 45154532 (1982).
  26. Kouwenhoven, L. P. et al. in NATO Advanced Study Institute on Mesoscopic Electron Transport E345 edn (eds Sohn, L. L., Kouwenhoven, L. P. &Schön, G.) 105214 (1997).

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Affiliations

  1. Department of Physics and Frederick Seitz Materials Research Laboratory University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

    • Travis Dirks,
    • Taylor L. Hughes,
    • Siddhartha Lal,
    • Bruno Uchoa,
    • Yung-Fu Chen,
    • Cesar Chialvo,
    • Paul M. Goldbart &
    • Nadya Mason
  2. Present address: IISER-Kolkata, Mohanpur campus, West Bengal - 741252, India. (S.L.) School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA. (P.M.G.)

    • Siddhartha Lal &
    • Paul M. Goldbart

Contributions

T.D. and Y-F.C. carried out the experiments. C.C. helped fabricate the samples. T.D., T.L.H., S.L., B.U., P.M.G. and N.M. analysed the data and wrote the main paper. T.L.H., B.U. and P.M.G. wrote Supplementary Information.

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The authors declare no competing financial interests.

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