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Emergent SU(4) Kondo physics in a spin–charge-entangled double quantum dot

Abstract

Quantum impurity models, which describe how a local degree of freedom interacts with a continuum, are central to condensed-matter physics. Such models may be naturally implemented with quantum dots coupled to each other and to metallic leads. Here we detail a many-body Kondo state occurring when two quantum dots are coupled electrostatically. We use orbital state-resolved bias spectroscopy to demonstrate the entanglement of spin and charge between spatially separated orbitals of the Kondo state. Detailed agreement between transport measurements and numerical renormalization group calculations suggests an emergent SU(4) symmetry.

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Figure 1: Survey of conductance at orbital degeneracies.
Figure 2: Agreement between experimental data and NRG calculations.
Figure 3: Universal scaling of the conductance.
Figure 4: Orbital state-resolved bias spectroscopy of the SU(4) Kondo resonance.

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References

  1. Coleman, P. Handbook of Magnetism and Advanced Magnetic Materials Vol. 1 (Wiley, 2007).

    Google Scholar 

  2. Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, 1997).

    Google Scholar 

  3. Dzero, M., Sun, K., Galitski, V. & Coleman, P. Topological Kondo insulators. Phys. Rev. Lett. 104, 106408 (2010).

    Article  ADS  Google Scholar 

  4. Zhang, X. et al. Hybridization, inter-ion correlation, and surface states in the Kondo insulator SmB6 . Phys. Rev. X 3, 011011 (2013).

    Google Scholar 

  5. Cox, D. L. & Zawadowski, A. Exotic Kondo Effects in Metals: Magnetic Ions in A Crystalline Electric Field and Tunneling Centres (Taylor & Francis, 1999).

    Google Scholar 

  6. Potok, R. M., Rau, I. G., Shtrikman, H., Oreg, Y. & Goldhaber-Gordon, D. Observation of the two-channel Kondo effect. Nature 446, 167–171 (2007).

    Article  ADS  Google Scholar 

  7. Goldhaber-Gordon, D. et al. The Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998).

    Article  ADS  Google Scholar 

  8. Cronenwett, S. M., Oosterkamp, T. H. & Kouwenhoven, L. P. A tunable Kondo effect in quantum dots. Science 281, 540–544 (1998).

    Article  ADS  Google Scholar 

  9. Goldhaber-Gordon, D. et al. From the Kondo regime to the mixed-valence regime in a single-electron transistor. Phys. Rev. Lett. 81, 5225–5228 (1998).

    Article  ADS  Google Scholar 

  10. Nygård, J., Cobden, D. H. & Lindelof, P. E. Kondo physics in carbon nanotubes. Nature 408, 342–346 (2000).

    Article  ADS  Google Scholar 

  11. Lee, M., Williams, J. R., Zhang, S., Frisbie, C. D. & Goldhaber-Gordon, D. Electrolyte gate-controlled Kondo effect in SrTiO3 . Phys. Rev. Lett. 107, 256601 (2011).

    Article  ADS  Google Scholar 

  12. Kretinin, A. V. et al. Spin-1/2 Kondo effect in an InAs nanowire quantum dot: Unitary limit, conductance scaling, and Zeeman splitting. Phys. Rev. B 84, 245316 (2011).

    Article  ADS  Google Scholar 

  13. Jespersen, T., Aagesen, M., Sørensen, C., Lindelof, P. & Nygård, J. Kondo physics in tunable semiconductor nanowire quantum dots. Phys. Rev. B 74, 233304 (2006).

    Article  ADS  Google Scholar 

  14. Madhavan, V., Chen, W., Jamneala, T., Crommie, M. F. & Wingreen, N. S. Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance. Science 280, 567–569 (1998).

    Article  ADS  Google Scholar 

  15. Li, J., Schneider, W-D., Berndt, R. & Delley, B. Kondo scattering observed at a single magnetic impurity. Phys. Rev. Lett. 80, 2893–2896 (1998).

    Article  ADS  Google Scholar 

  16. Otte, A. F. et al. The role of magnetic anisotropy in the Kondo effect. Nature Phys. 4, 847–850 (2008).

    Article  ADS  Google Scholar 

  17. Sasaki, S., Amaha, S., Asakawa, N., Eto, M. & Tarucha, S. Enhanced Kondo effect via tuned orbital degeneracy in a spin 1/2 artificial atom. Phys. Rev. Lett. 93, 017205 (2004).

    Article  ADS  Google Scholar 

  18. Parks, J. J. et al. Tuning the Kondo effect with a mechanically controllable break junction. Phys. Rev. Lett. 99, 026601 (2007).

    Article  ADS  Google Scholar 

  19. Zaránd, G., Brataas, A. & Goldhaber-Gordon, D. Kondo effect and spin filtering in triangular artificial atoms. Solid State Commun. 126, 463–466 (2003).

    Article  ADS  Google Scholar 

  20. Borda, L., Zaránd, G., Hofstetter, W., Halperin, B. I. & von Delft, J. SU(4) Fermi liquid state and spin filtering in a double quantum dot system. Phys. Rev. Lett. 90, 026602 (2003).

    Article  ADS  Google Scholar 

  21. Le Hur, K. & Simon, P. Smearing of charge fluctuations in a grain by spin-flip assisted tunneling. Phys. Rev. B 67, 201308(R) (2003).

    Article  ADS  Google Scholar 

  22. Le Hur, K., Simon, P. & Borda, L. Maximized orbital and spin Kondo effects in a single-electron transistor. Phys. Rev. B 69, 045326 (2004).

    Article  ADS  Google Scholar 

  23. Eto, M. Enhancement of Kondo effect in multilevel quantum dots. J. Phys. Soc. Jpn 74, 95–102 (2005).

    Article  ADS  Google Scholar 

  24. López, R. et al. Probing spin and orbital Kondo effects with a mesoscopic interferometer. Phys. Rev. B 71, 115312 (2005).

    Article  ADS  Google Scholar 

  25. Sato, T. & Eto, M. Numerical renormalization group studies of SU(4) Kondo effect in quantum dots. Physica E 29, 652–5 (2005).

    Article  ADS  Google Scholar 

  26. Le Hur, K., Simon, P. & Loss, D. Transport through a quantum dot with SU(4) Kondo entanglement. Phys. Rev. B 75, 035332 (2007).

    Article  ADS  Google Scholar 

  27. Choi, M.-S., López, R. & Aguado, R. SU(4) Kondo effect in carbon nanotubes. Phys. Rev. Lett. 95, 067204 (2005).

    Article  ADS  Google Scholar 

  28. Anders, F., Logan, D., Galpin, M. & Finkelstein, G. Zero-bias conductance in carbon nanotube quantum dots. Phys. Rev. Lett. 100, 086809 (2008).

    Article  ADS  Google Scholar 

  29. Jarillo-Herrero, P. et al. Orbital Kondo effect in carbon nanotubes. Nature 434, 484–8 (2005).

    Article  ADS  Google Scholar 

  30. Makarovski, A., Zhukov, A., Liu, J. & Finkelstein, G. SU(2) and SU(4) Kondo effects in carbon nanotube quantum dots. Phys. Rev. B 75, 241407 (2007).

    Article  ADS  Google Scholar 

  31. Delattre, T. et al. Noisy Kondo impurities. Nature Phys. 5, 208–212 (2009).

    Article  ADS  Google Scholar 

  32. Makarovski, A., Liu, J. & Finkelstein, G. Evolution of transport regimes in carbon nanotube quantum dots. Phys. Rev. Lett. 99, 066801 (2007).

    Article  ADS  Google Scholar 

  33. Tettamanzi, G. C. et al. Magnetic-field probing of an SU(4) Kondo resonance in a single-atom transistor. Phys. Rev. Lett. 108, 046803 (2012).

    Article  ADS  Google Scholar 

  34. Lansbergen, G. P. et al. Tunable Kondo effect in a single donor atom. Nano Lett. 10, 455–460 (2010).

    Article  ADS  Google Scholar 

  35. Nishikawa, Y., Hewson, A. C., Crow, D. J. G. & Bauer, J. Analysis of low energy response and possible emergent SU(4) Kondo state in a quantum dot. http://arxiv.org/abs/1309.1715 (2013).

  36. Amasha, S. et al. Pseudospin-resolved transport spectroscopy of the Kondo effect in a double quantum dot. Phys. Rev. Lett. 110, 046604 (2013).

    Article  ADS  Google Scholar 

  37. Van der Wiel, W. G. et al. Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1–22 (2002).

    Article  ADS  Google Scholar 

  38. Hübel, A., Held, K., Weis, J. & von Klitzing, K. Correlated electron tunneling through two separate quantum dot systems with strong capacitive interdot coupling. Phys. Rev. Lett. 101, 186804 (2008).

    Article  ADS  Google Scholar 

  39. Okazaki, Y., Sasaki, S. & Muraki, K. Spin-orbital Kondo effect in a parallel double quantum dot. Phys. Rev. B 84, 161305(R) (2011).

    Article  ADS  Google Scholar 

  40. Büsser, C. A., Feiguin, A. E. & Martins, G. B. Electrostatic control over polarized currents through the spin-orbital Kondo effect. Phys. Rev. B 85, 241310(R) (2012).

    Article  ADS  Google Scholar 

  41. Galpin, M. R., Logan, D. E. & Krishnamurthy, H. R. Renormalization group study of capacitively coupled double quantum dots. J. Phys. Condens. Matter 18, 6545–6470 (2006).

    Article  ADS  Google Scholar 

  42. Galpin, M. R., Logan, D. E. & Krishnamurthy, H. R. Quantum phase transition in capacitively coupled double quantum dots. Phys. Rev. Lett. 94, 186406 (2005).

    Article  ADS  Google Scholar 

  43. Meir, Y., Wingreen, N. S. & Lee, P. A. Low-temperature transport through a quantum dot: The Anderson model out of equilibrium. Phys. Rev. Lett. 70, 2601–2604 (1993).

    Article  ADS  Google Scholar 

  44. Kogan, A. et al. Measurements of Kondo and spin splitting in single-electron transistors. Phys. Rev. Lett. 93, 166602 (2004).

    Article  ADS  Google Scholar 

  45. Kaminski, A., Nazarov, Yu. V. & Glazman, L. I. Suppression of the Kondo effect in a quantum dot by external irradiation. Phys. Rev. Lett. 83, 384–387 (1999).

    Article  ADS  Google Scholar 

  46. Hayashi, T., Fujisawa, T., Cheong, H., Jeong, Y. & Hirayama, Y. Coherent manipulation of electronic states in a double quantum dot. Phys. Rev. Lett. 91, 226804 (2003).

    Article  ADS  Google Scholar 

  47. Petersson, K. D., Petta, J. R., Lu, H. & Gossard, A. C. Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010).

    Article  ADS  Google Scholar 

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Acknowledgements

We are grateful to Y. Oreg, A. Carmi, J. König, A. G. Moghaddam, G. B. Martins, C. A. Büsser, A. E. Feiguin, J. Bauer, A. C. Hewson and L. Peeters for discussions. Experimental work was supported by the NSF under DMR-0906062, by the US–Israel BSF grant No. 2008149, and most recently by the Gordon and Betty Moore Foundation through Grant GBMF3429. A.J.K. acknowledges a Stanford Graduate Fellowship. G.Z. and C.P.M. acknowledge support from Hungarian Grant Nos. K105149 and CNK80991. C.P.M. was financially supported by UEFISCDI under French-Romanian Grant DYMESYS, Contract No. PN-II-ID-JRP-2011-1. I.W. acknowledges support from EU grant No. CIG-303 689 and MSHE grant No. IP2011 059471. NRG calculations were performed at Poznań Supercomputing and Networking Center.

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Contributions

A.J.K., S.A., G.Z. and D.G-G. designed the experiment. A.J.K. and S.A. performed the measurements, with substantial contributions from I.G.R. I.W., C.P.M. and G.Z. performed the NRG calculations. C.P.M. and I.W. contributed equally to the theoretical analysis. A.J.K., S.A., C.P.M., I.W., G.Z. and D.G-G. analysed the data. S.A. designed and fabricated the devices, with electron-beam lithography done by J.A.K., using heterostructures grown by H.S. A.J.K. wrote the paper with critical review provided by all other authors.

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Correspondence to D. Goldhaber-Gordon.

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Keller, A., Amasha, S., Weymann, I. et al. Emergent SU(4) Kondo physics in a spin–charge-entangled double quantum dot. Nature Phys 10, 145–150 (2014). https://doi.org/10.1038/nphys2844

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