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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References
Coleman, P. Handbook of Magnetism and Advanced Magnetic Materials Vol. 1 (Wiley, 2007).
Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, 1997).
Dzero, M., Sun, K., Galitski, V. & Coleman, P. Topological Kondo insulators. Phys. Rev. Lett. 104, 106408 (2010).
Zhang, X. et al. Hybridization, inter-ion correlation, and surface states in the Kondo insulator SmB6 . Phys. Rev. X 3, 011011 (2013).
Cox, D. L. & Zawadowski, A. Exotic Kondo Effects in Metals: Magnetic Ions in A Crystalline Electric Field and Tunneling Centres (Taylor & Francis, 1999).
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).
Goldhaber-Gordon, D. et al. The Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998).
Cronenwett, S. M., Oosterkamp, T. H. & Kouwenhoven, L. P. A tunable Kondo effect in quantum dots. Science 281, 540–544 (1998).
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).
Nygård, J., Cobden, D. H. & Lindelof, P. E. Kondo physics in carbon nanotubes. Nature 408, 342–346 (2000).
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).
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).
Jespersen, T., Aagesen, M., Sørensen, C., Lindelof, P. & Nygård, J. Kondo physics in tunable semiconductor nanowire quantum dots. Phys. Rev. B 74, 233304 (2006).
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).
Li, J., Schneider, W-D., Berndt, R. & Delley, B. Kondo scattering observed at a single magnetic impurity. Phys. Rev. Lett. 80, 2893–2896 (1998).
Otte, A. F. et al. The role of magnetic anisotropy in the Kondo effect. Nature Phys. 4, 847–850 (2008).
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).
Parks, J. J. et al. Tuning the Kondo effect with a mechanically controllable break junction. Phys. Rev. Lett. 99, 026601 (2007).
Zaránd, G., Brataas, A. & Goldhaber-Gordon, D. Kondo effect and spin filtering in triangular artificial atoms. Solid State Commun. 126, 463–466 (2003).
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).
Le Hur, K. & Simon, P. Smearing of charge fluctuations in a grain by spin-flip assisted tunneling. Phys. Rev. B 67, 201308(R) (2003).
Le Hur, K., Simon, P. & Borda, L. Maximized orbital and spin Kondo effects in a single-electron transistor. Phys. Rev. B 69, 045326 (2004).
Eto, M. Enhancement of Kondo effect in multilevel quantum dots. J. Phys. Soc. Jpn 74, 95–102 (2005).
López, R. et al. Probing spin and orbital Kondo effects with a mesoscopic interferometer. Phys. Rev. B 71, 115312 (2005).
Sato, T. & Eto, M. Numerical renormalization group studies of SU(4) Kondo effect in quantum dots. Physica E 29, 652–5 (2005).
Le Hur, K., Simon, P. & Loss, D. Transport through a quantum dot with SU(4) Kondo entanglement. Phys. Rev. B 75, 035332 (2007).
Choi, M.-S., López, R. & Aguado, R. SU(4) Kondo effect in carbon nanotubes. Phys. Rev. Lett. 95, 067204 (2005).
Anders, F., Logan, D., Galpin, M. & Finkelstein, G. Zero-bias conductance in carbon nanotube quantum dots. Phys. Rev. Lett. 100, 086809 (2008).
Jarillo-Herrero, P. et al. Orbital Kondo effect in carbon nanotubes. Nature 434, 484–8 (2005).
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).
Delattre, T. et al. Noisy Kondo impurities. Nature Phys. 5, 208–212 (2009).
Makarovski, A., Liu, J. & Finkelstein, G. Evolution of transport regimes in carbon nanotube quantum dots. Phys. Rev. Lett. 99, 066801 (2007).
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).
Lansbergen, G. P. et al. Tunable Kondo effect in a single donor atom. Nano Lett. 10, 455–460 (2010).
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).
Amasha, S. et al. Pseudospin-resolved transport spectroscopy of the Kondo effect in a double quantum dot. Phys. Rev. Lett. 110, 046604 (2013).
Van der Wiel, W. G. et al. Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1–22 (2002).
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).
Okazaki, Y., Sasaki, S. & Muraki, K. Spin-orbital Kondo effect in a parallel double quantum dot. Phys. Rev. B 84, 161305(R) (2011).
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).
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).
Galpin, M. R., Logan, D. E. & Krishnamurthy, H. R. Quantum phase transition in capacitively coupled double quantum dots. Phys. Rev. Lett. 94, 186406 (2005).
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).
Kogan, A. et al. Measurements of Kondo and spin splitting in single-electron transistors. Phys. Rev. Lett. 93, 166602 (2004).
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).
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).
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).
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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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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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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DOI: https://doi.org/10.1038/nphys2844
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