ABSTRACT
We report thermally activated transport resonances for biases below the superconducting energy gap in a carbon nanotube quantum dot (QD) device with a superconducting Pb and a normal metal contact. These resonances are due to the superconductor's finite quasi-particle population at elevated temperatures and can only be observed when the QD life-time broadening is considerably smaller than the gap. This condition is fulfilled in our QD devices with optimized Pd/Pb/In multi-layer contacts, which result in reproducibly large and “clean” superconducting transport gaps with a strong conductance suppression for subgap biases. We show that these gaps close monotonically with increasing magnetic field and temperature. The accurate description of the subgap resonances by a simple resonant tunneling model illustrates the ideal characteristics of the reported Pb contacts and gives an alternative access to the tunnel coupling strengths in a QD.
This work was financially supported by the Swiss National Science Foundation (SNF), the Swiss Nanoscience Institute (SNI), the Swiss NCCR QSIT, the ERC Project QUEST, and the EU FP7 Project SE2ND.
REFERENCES
- 1. M. R. Gräber, T. Nussbaumer, W. Belzig, and C. Schönenberger, Nanotechnology 15, S479 (2004). https://doi.org/10.1088/0957-4484/15/7/056, Google ScholarCrossref, ISI
- 2. V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Science 336, 1003 (2012). https://doi.org/10.1126/science.1222360, Google ScholarCrossref, ISI
- 3. S. Das Sarma, M. Freedman, and C. Nayak, NPJ Quantum Inf. 1, 15001 (2015). https://doi.org/10.1038/npjqi.2015.1, Google ScholarCrossref
- 4. P. Recher, E. V. Sukhorukov, and D. Loss, Phys. Rev. B 63, 165314 (2001). https://doi.org/10.1103/PhysRevB.63.165314, Google ScholarCrossref, ISI
- 5. L. Hofstetter, S. Csonka, J. Nygård, and C. Schönenberger, Nature 461, 960 (2009). https://doi.org/10.1038/nature08432, Google ScholarCrossref
- 6. L. G. Herrmann, F. Portier, P. Roche, A. Levy Yeyati, T. Kontos, and C. Strunk, Phys. Rev. Lett. 104, 026801 (2010). https://doi.org/10.1103/PhysRevLett.104.026801, Google ScholarCrossref, ISI
- 7. J. Schindele, A. Baumgartner, and C. Schönenberger, Phys. Rev. Lett. 109, 157002 (2012). https://doi.org/10.1103/PhysRevLett.109.157002, Google ScholarCrossref, ISI
- 8. A. Das, Y. Ronen, M. Heiblum, D. Mahalu, A. V. Kretinin, and H. Shtrikman, Nat. Commun. 3, 1165 (2012). https://doi.org/10.1038/ncomms2169, Google ScholarCrossref, ISI
- 9. J. Gramich, A. Baumgartner, and C. Schönenberger, Phys. Rev. Lett. 115, 216801 (2015). https://doi.org/10.1103/PhysRevLett.115.216801, Google ScholarCrossref
- 10. J.-D. Pillet, C. H. L. Quay, P. Morfin, C. Bena, A. Levy Yeyati, and P. Joyez, Nat. Phys. 6, 965 (2010). https://doi.org/10.1038/nphys1811, Google ScholarCrossref
- 11. T. Dirks, T. L. Hughes, S. Lal, B. Uchoa, Y.-F. Chen, C. Chialvo, P. M. Goldbart, and N. Mason, Nat. Phys. 7, 386 (2011). https://doi.org/10.1038/nphys1911, Google ScholarCrossref
- 12. E. J. H. Lee, X. Jiang, M. Houzet, R. Aguado, C. M. Lieber, and S. De Franceschi, Nat. Nanotechnol. 9, 79 (2014). https://doi.org/10.1038/nnano.2013.267, Google ScholarCrossref, ISI
- 13. J. Schindele, A. Baumgartner, R. Maurand, M. Weiss, and C. Schönenberger, Phys. Rev. B 89, 045422 (2014). https://doi.org/10.1103/PhysRevB.89.045422, Google ScholarCrossref, ISI
- 14. L. Bretheau, Ç. Ö. Girit, H. Pothier, D. Esteve, and C. Urbina, Nature 499, 312 (2013). https://doi.org/10.1038/nature12315, Google ScholarCrossref
- 15. C. Janvier, L. Tosi, L. Bretheau, Ç. Ö. Girit, M. Stern, P. Bertet, P. Joyez, D. Vion, D. Esteve, M. F. Goffman, H. Pothier, and C. Urbina, Science 349, 1199 (2015). https://doi.org/10.1126/science.aab2179, Google ScholarCrossref
- 16. M. Gaass, S. Pfaller, T. Geiger, A. Donarini, M. Grifoni, A. K. Hüttel, and C. Strunk, Phys. Rev. B 89, 241405 (2014). https://doi.org/10.1103/PhysRevB.89.241405, Google ScholarCrossref
- 17. S. Ratz, A. Donarini, D. Steininger, T. Geiger, A. Kumar, A. K. Hüttel, C. Strunk, and M. Grifoni, New J. Phys. 16, 123040 (2014). https://doi.org/10.1088/1367-2630/16/12/123040, Google ScholarCrossref
- 18. A. P. Higginbotham, S. M. Albrecht, G. Kirsanskas, W. Chang, F. Kuemmeth, P. Krogstrup, T. S. Jespersen, J. Nygård, K. Flensberg, and C. M. Marcus, Nat. Phys. 11, 1017 (2015). https://doi.org/10.1038/nphys3461, Google ScholarCrossref
- 19. W. Chang, S. M. Albrecht, T. S. Jespersen, F. Kuemmeth, P. Krogstrup, J. Nygård, and C. M. Marcus, Nat. Nanotechnol. 10, 232 (2015). https://doi.org/10.1038/nnano.2014.306, Google ScholarCrossref, ISI
- 20. M. Taupin, P. Krogstrup, H. Q. Nguyen, E. Mannila, S. M. Albrecht, J. Nygård, C. M. Marcus, and J. P. Pekola, e-print arXiv:1601.01149. Google Scholar
- 21. K. Grove-Rasmussen, H. I. Jørgensen, B. M. Andersen, J. Paaske, T. S. Jespersen, J. Nygård, K. Flensberg, and P. E. Lindelof, Phys. Rev. B 79, 134518 (2009). https://doi.org/10.1103/PhysRevB.79.134518, Google ScholarCrossref
- 22. G. Fülöp, F. Domínguez, S. d'Hollosy, A. Baumgartner, P. Makk, M. H. Madsen, V. A. Guzenko, J. Nygård, C. Schönenberger, A. Levy Yeyati, and S. Csonka, Phys. Rev. Lett. 115, 227003 (2015). https://doi.org/10.1103/PhysRevLett.115.227003, Google ScholarCrossref
- 23. C. P. Poole, Handbook of Superconductivity, edited by C. P. Poole ( Academic Press, San Diego, CA, 2000). Google ScholarCrossref
- 24. Y.-F. Chen, T. Dirks, G. Al-Zoubi, N. O. Birge, and N. Mason, Phys. Rev. Lett. 102, 036804 (2009). https://doi.org/10.1103/PhysRevLett.102.036804, Google ScholarCrossref
- 25. N. Bronn and N. Mason, Phys. Rev. B 88, 161409 (2013). https://doi.org/10.1103/PhysRevB.88.161409, Google ScholarCrossref
- 26. T. Dirks, Y.-F. Chen, N. O. Birge, and N. Mason, Appl. Phys. Lett. 95, 192103 (2009). https://doi.org/10.1063/1.3253705, Google ScholarScitation, ISI
- 27. I. V. Borzenets, Y. Shimazaki, G. F. Jones, M. F. Craciun, S. Russo, Y. Yamamoto, and S. Tarucha, Sci. Rep. 6, 23051 (2016). https://doi.org/10.1038/srep23051, Google ScholarCrossref
- 28. C. B. Whan and T. P. Orlando, Phys. Rev. B 54, R5255 (1996). https://doi.org/10.1103/PhysRevB.54.R5255, Google ScholarCrossref
- 29. S. Pfaller, A. Donarini, and M. Grifoni, Phys. Rev. B 87, 155439 (2013). https://doi.org/10.1103/PhysRevB.87.155439, Google ScholarCrossref
- 30. S. Skalski, O. Betbeder-Matibet, and P. R. Weiss, Phys. Rev. 136, A1500 (1964). https://doi.org/10.1103/PhysRev.136.A1500, Google ScholarCrossref, ISI
- 31. R. Yang, L. Zhang, Y. Wang, Z. Shi, D. Shi, H. Gao, E. Wang, and G. Zhang, Adv. Mater. 22, 4014 (2010). https://doi.org/10.1002/adma.201000618, Google ScholarCrossref
- 32. J. Samm, J. Gramich, A. Baumgartner, M. Weiss, and C. Schönenberger, J. Appl. Phys. 115, 174309 (2014). https://doi.org/10.1063/1.4874919, Google ScholarScitation
- 33. J. M. Eldridge, Y. J. Van der Meulen, and D. W. Dong, Thin Solid Films 12, 447 (1972). https://doi.org/10.1016/0040-6090(72)90111-3, Google ScholarCrossref
- 34. J. Kim, V. Chua, G. A. Fiete, H. Nam, A. H. MacDonald, and C.-K. Shih, Nat. Phys. 8, 464 (2012). https://doi.org/10.1038/nphys2287, Google ScholarCrossref
- 35. L. Serrier-Garcia, J. C. Cuevas, T. Cren, C. Brun, V. Cherkez, F. Debontridder, D. Fokin, F. S. Bergeret, and D. Roditchev, Phys. Rev. Lett. 110, 157003 (2013). https://doi.org/10.1103/PhysRevLett.110.157003, Google ScholarCrossref
- 36. A. Levy Yeyati, J. C. Cuevas, A. López-Dávalos, and A. Martín-Rodero, Phys. Rev. B 55, R6137 (1997). https://doi.org/10.1103/PhysRevB.55.R6137, Google ScholarCrossref, ISI
- 37. D. J. Thouless, Phys. Rev. 117, 1256 (1960). https://doi.org/10.1103/PhysRev.117.1256, Google ScholarCrossref
- 38. D. H. Douglass, Jr. and L. M. Falicov, “ The superconducting energy gap,” in Progress in Low Temperature Physics, edited by C. Gorter ( Elsevier, 1964), Vol. 4, pp. 97–193. Google Scholar
- 39. R. F. Gasparovic, B. N. Taylor, and R. E. Eck, Solid State Commun. 4, 59 (1966). https://doi.org/10.1016/0038-1098(66)90106-2, Google ScholarCrossref
- 40.We use the Drude model to estimate the mean free path of our Pb strips from the measured low-temperature Pb strip resistivity. Assuming the bulk literature values of Pb23 for the coherence length ξ∞ ∼ 90 nm and the penetration depth λ∞ ∼ 40 nm in the clean limit (l = ∞), we estimate the coherence length and penetration depth of our Pb strips using the interpolation formulae suitable for the regime and ,42 respectively.
- 41.We use the equations and of Ref. 30, valid in the dirty limit l ≪ ξ and for , to calculate the dependence of the visible transport gap (the spectral quasiparticle gap) Δ as a function of B. Here, is the order parameter, Δ0 the experimentally determined transport gap at B = 0 and at base temperature, and the pair-breaking parameter with the exponent n.30,42 Note that we use Bc as adjustable parameter so that vanishes at the experimentally determined values.
- 42. M. Tinkham, Introduction to Superconductivity, 2nd ed. ( Dover, 2004). Google Scholar
- 43.We ascribe the small central subgap conductance peak between TL and TR to the thermally broadened DOS in the S contact, coinciding with . The analysis at VSD = ±1 mV shows that this finite subgap conductance at elevated temperatures has no influence on our analysis.
- 44. We carefully controlled that no structures are lost or created in the averaging procedure. Google Scholar
- 45.In the studied temperature range , the closing of the transport gap for plays already a significant role.
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