Some of the most intriguing problems in solid-state physics arise when the motion of one electron dramatically affects the motion of surrounding electrons. Traditionally, such highly correlated electron systems have been studied mainly in materials with complex transition metal chemistry1,2. Over the past decade, researchers have learned to confine one or a few electrons within a nanometre-scale semiconductor ‘artificial atom’, and to understand and control this simple system in detail3. Here we combine artificial atoms to create a highly correlated electron system within a nano-engineered semiconductor structure3. We tune the system in situ through a quantum phase transition between two distinct states, each a version of the Kondo state4, in which a bound electron interacts with surrounding mobile electrons. The boundary between these competing Kondo states is a quantum critical point—namely, the exotic and previously elusive two-channel Kondo state5,6, in which electrons in two reservoirs are entangled through their interaction with a single localized spin.
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Pruschke, T., Jarrel, M. & Freericks, J. Anomalous normal-state properties of high T c superconductors: Intrinsic properties of strongly correlated electron systems? Adv. Phys. 44, 187–210 (1995)
Cox, D. L. & Zawadowski, A. Exotic Kondo effects in metals: magnetic ions in a crystalline electric field and tunnelling centres. Adv. Phys. 47, 599–942 (1998)
Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Preprint at 〈http://arxiv.org/cond-mat/0610433〉 (2006)
Oreg, Y. & Goldhaber-Gordon, D. Two-channel Kondo effect in a modified single electron transistor. Phys. Rev. Lett. 90, 136602 (2003)
Wilson, K. G. The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773–840 (1974)
Nozières, P. & Blandin, A. Kondo effect in real metals. J. Phys. 41, 193–211 (1980)
Zawadowski, A. Kondo-like state in a simple model for metallic glasses. Phys. Rev. Lett. 45, 211–214 (1980)
Goldhaber-Gordon, D. et al. Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998)
Grobis, M., Rau, I. G., Potok, R. M. & Goldhaber-Gordon, D. Kondo effect in mesoscopic quantum dots. Preprint at 〈http://arxiv.org/cond-mat/0611480〉 (2006)
Kondo, J. Resistance minimum in dilute magnetic alloys. Prog, Theor. Phys. 32, 37–49 (1964)
Affleck, I. & Ludwig, A. W. W. Exact conformal-field-theory results on the multichannel Kondo effect: single-fermion Green’s function, self-energy, and resistivity. Phys. Rev. B 48, 7297–7321 (1993)
Cox, D. L. Quadrupolar Kondo effect in uranium heavy-electron materials. Phys. Rev. Lett. 59, 1240–1243 (1987)
Seaman, C. L. et al. Evidence for non-Fermi-liquid behavior in the Kondo alloy Y1-xUxPd3 . Phys. Rev. Lett. 67, 2882–2885 (1991)
Besnus, M. J. et al. Specific-heat and NMR of the Kondo system YbPd2Si2 . J. Magn. Magn. Mater. 76–7, 471–472 (1988)
Ralph, D. C. & Buhrman, R. A. Observations of Kondo scattering without magnetic-impurities — a point contact study of 2-level tunneling systems in metals. Phys. Rev. Lett. 69, 2118–2121 (1992)
Ralph, D. C., Ludwig, A. W. W., von Delft, J. & Buhrman, R. A. 2-channel Kondo scaling in conductance signals from 2-level tunneling systems. Phys. Rev. Lett. 72, 1064–1067 (1994)
Cichorek, T. et al. Two-channel Kondo effect in glasslike ThAsSe. Phys. Rev. Lett. 94, 236603 (2005)
Glazman, L. I. & Raikh, M. E. Resonant Kondo transparency of a barrier with quasilocal impurity states. JETP Lett. 47, 452–455 (1988)
Costi, T. A. & Hewson, A. C. Transport coefficients of the Anderson model via the numerical renormalization group. J. Phys. Condens. Matter 6, 2519–2558 (1994)
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)
Göres, J. et al. Fano resonances in electronic transport through a single-electron transistor. Phys. Rev. B 62, 2188–2194 (2000)
Majumdar, K., Schiller, A. & Hershfield, S. Nonequilibrium Kondo impurity: Perturbation about an exactly solvable point. Phys. Rev. B 57, 2991–2999 (1998)
Hettler, M. H., Kroha, J. & Hershfield, S. Nonlinear conductance for the two channel Anderson model. Phys. Rev. Lett. 73, 1967–1970 (1994)
Oreg, Y. & Goldhaber-Gordon, D. Physics of Zero and One Dimensional Nanoscopic Systems (Springer Series in Solid State Sciences, Springer, in the press).
Pustilnik, M., Borda, L., Glazman, L. & von Delft, J. Quantum phase transition in a two-channel-Kondo quantum dot device. Phys. Rev. B 69, 115316 (2004)
von Delft, J., Ludwig, A. W. W. & Ambegaokar, V. The 2-channel Kondo model. II. CFT calculation of non-equilibrium conductance through a nanoconstriction containing 2-channel Kondo impurities. Ann. Phys. 273, 175–241 (1999)
Florens, S. & Rosch, A. Climbing the entropy barrier: Driving the single- towards the multichannel Kondo effect by a weak Coulomb blockade of the leads. Phys. Rev. Lett. 92, 216601 (2004)
Lebanon, E., Schiller, A. & Anders, F. B. Enhancement of the two-channel Kondo effect in single-electron boxes. Phys. Rev. B 68, 155301 (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)
Haldane, F. D. M. Scaling theory of the asymmetric Anderson model. Phys. Rev. Lett. 40, 416–419 (1978)
We thank A. Schiller, E. Lebanon, F. Anders, I. Affleck, T. Costi, L. Glazman, K. Le Hur, C. Marcus, M. Pustilnik, E. Sela, J. von Delft and G. Zarand for discussions. E. Lebanon and F. Anders also performed NRG calculations that gave us crucial intuition regarding where our experimental system was in parameter space. S. Roy helped us understand how to perform nonlinear fits to determine the exponents α and α2 for the energy dependence in both 1CK and 2CK regimes. This work was supported by an NSF CAREER Award, a US-Israel BSF Award, DIP and ISF. D.G.-G. acknowledges Fellowships from the Sloan and Packard Foundations, and a Research Corporation Research Innovation Award. R.M.P. was supported by an ARO Graduate Fellowship during the early stages of this work.
Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.
This file contains Supplementary Discussion of data analysis and interpretation with brief mention of measurement techniques and relations to other proposed experimental two-channel Kondo systems. The file also contains Supplementary Figures S1-S7 with Legends and additional references. (PDF 382 kb)
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Potok, R., Rau, I., Shtrikman, H. et al. Observation of the two-channel Kondo effect. Nature 446, 167–171 (2007). https://doi.org/10.1038/nature05556
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