Letter | Published:

Universal Fermi liquid crossover and quantum criticality in a mesoscopic system

Nature volume 526, pages 237240 (08 October 2015) | Download Citation

Abstract

Quantum critical systems derive their finite-temperature properties from the influence of a zero-temperature quantum phase transition1. The paradigm is essential for understanding unconventional high-Tc superconductors and the non-Fermi liquid properties of heavy fermion compounds. However, the microscopic origins of quantum phase transitions in complex materials are often debated. Here we demonstrate experimentally, with support from numerical renormalization group calculations, a universal crossover from quantum critical non-Fermi liquid behaviour to distinct Fermi liquid ground states in a highly controllable quantum dot device. Our device realizes the non-Fermi liquid two-channel Kondo state2,3, based on a spin-1/2 impurity exchange-coupled equally to two independent electronic reservoirs4. On detuning the exchange couplings we observe the Fermi liquid scale T*, at energies below which the spin is screened conventionally by the more strongly coupled channel. We extract a quadratic dependence of T* on gate voltage close to criticality, and validate an asymptotically exact description of the universal crossover between strongly correlated non-Fermi liquid and Fermi liquid states5,6.

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References

  1. 1.

    Quantum Phase Transitions 2nd edn (Cambridge Univ. Press, 2011)

  2. 2.

    & Two-channel Kondo effect in a modified single electron transistor. Phys. Rev. Lett. 90, 136602 (2003)

  3. 3.

    , , , & Observation of the two-channel Kondo effect. Nature 446, 167–171 (2007)

  4. 4.

    & Kondo effect in real metals. J. Phys. (Paris) 41, 193–211 (1980)

  5. 5.

    , & Exact crossover Green function in the two-channel and two-impurity Kondo models. Phys. Rev. Lett. 106, 147202 (2011)

  6. 6.

    & Universal low-temperature crossover in two-channel Kondo models. Phys. Rev. B 85, 235127 (2012)

  7. 7.

    , & Quantum criticality in heavy-fermion metals. Nature Phys. 4, 186–197 (2008)

  8. 8.

    , , & How do Fermi liquids get heavy and die? J. Phys. Condens. Matter 13, R723–R738 (2001)

  9. 9.

    et al. Quantum phase transition in a resonant level coupled to interacting leads. Nature 488, 61–64 (2012)

  10. 10.

    et al. Observation of Majorana quantum critical behaviour in a resonant level coupled to a dissipative environment. Nature Phys. 9, 732–737 (2013)

  11. 11.

    , & The Kondo effect in an artificial quantum dot molecule. Science 293, 2221–2223 (2001)

  12. 12.

    et al. A tunable two-impurity Kondo system in an atomic point contact. Nature Phys. 7, 901–906 (2011)

  13. 13.

    et al. Tunable Kondo physics in a carbon nanotube double quantum dot. Phys. Rev. Lett. 109, 156804 (2012)

  14. 14.

    & Mapping of the two-channel Kondo problem to a resonant-level model. Phys. Rev. B 46, 10812–10817 (1992)

  15. 15.

    Quadrupolar Kondo effect in uranium heavy-electron materials? Phys. Rev. Lett. 59, 1240–1243 (1987)

  16. 16.

    et al. Evidence for non-Fermi-liquid behavior in the Kondo alloy Y1−xUxPd3. Phys. Rev. Lett. 67, 2882–2885 (1991)

  17. 17.

    et al. Specific heat and NMR of the Kondo system YbPd2Si2. J. Magn. Magn. Mater. 76–77, 471–472 (1988)

  18. 18.

    , , & 2-channel Kondo scaling in conductance signals from 2-level tunneling systems. Phys. Rev. Lett. 72, 1064–1067 (1994)

  19. 19.

    et al. Two-channel Kondo effect in glasslike ThAsSe. Phys. Rev. Lett. 94, 236603 (2005)

  20. 20.

    & Two-channel Kondo effects in Al/AlOx/Sc planar tunnel junctions. Phys. Rev. B 79, 012411 (2009)

  21. 21.

    , , & Dynamical conductance in the two-channel Kondo regime of a double dot system. Phys. Rev. B 76, 155318 (2007)

  22. 22.

    , & Anderson-Yuval approach to the multichannel Kondo problem. Phys. Rev. B 51, 16088–16097 (1995)

  23. 23.

    , & Coulomb blockade and non-Fermi-liquid behavior in quantum dots. Phys. Rev. B 70, 201306(R) (2004)

  24. 24.

    , & Conductance in coupled quantum dots: indicator for a local quantum phase transition. In NIC Symposium Vol. 32, 191–199 (John von Neumann Institute for Computing, Jülich, 2006)

  25. 25.

    , & Enhancement of the two-channel Kondo effect in single-electron boxes. Phys. Rev. B 68, 155301 (2003)

  26. 26.

    & 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)

  27. 27.

    , , & Theory of inelastic scattering from quantum impurities. Phys. Rev. B 75, 235112 (2007)

  28. 28.

    Quantum fluctuations of the charge of a metal particle under the Coulomb blockade conditions. Sov. Phys. JETP 72, 892–899 (1991)

  29. 29.

    , & Maximized orbital and spin Kondo effects in a single-electron transistor. Phys. Rev. B 69, 045326 (2004)

  30. 30.

    , & Transport through a quantum dot with SU(4) Kondo entanglement. Phys. Rev. B 75, 035332 (2007)

  31. 31.

    , , & Transmission phase shifts of Kondo impurities. Phys. Rev. B 86, 115129 (2012)

  32. 32.

    , , , & Repairing nanoscale devices using electron-beam-induced deposition of platinum. J. Vac. Sci. Technol. B 33, 051803 (2015)

  33. 33.

    et al. Origin of switching noise in GaAs/AlxGa1−xAs lateral gated devices. Phys. Rev. B 72, 115331 (2005)

  34. 34.

    & Wide-band current preamplifier for conductance measurements with large input capacitance. Rev. Sci. Instrum. 83, 084704 (2012)

  35. 35.

    & Condensed Matter Field Theory 2nd edn (Cambridge Univ. Press, 2010)

  36. 36.

    , , & SU(3) Anderson impurity model: a numerical renormalization group approach exploiting non-Abelian symmetries. Phys. Rev. B 86, 195128 (2012)

  37. 37.

    Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Phys. Rev. B 44, 1646–1656 (1991)

  38. 38.

    & Prediction of the capacitance line shape in two-channel quantum dots. Phys. Rev. Lett. 95, 036801 (2005)

  39. 39.

    , & Two-channel Kondo physics in odd impurity chains. Phys. Rev. B 84, 035119 (2011)

  40. 40.

    The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773–840 (1975)

  41. 41.

    , , , & Manual for the Flexible DM-NRG Code. (2008)

  42. 42.

    & Kondo effect in real quantum dots. Phys. Rev. Lett. 87, 216601 (2001)

  43. 43.

    , & Numerical renormalization group method for quantum impurity systems. Rev. Mod. Phys. 80, 395–450 (2008)

  44. 44.

    & Sum-rule conserving spectral functions from the numerical renormalization group. Phys. Rev. Lett. 99, 076402 (2007)

  45. 45.

    , , & Density matrix numerical renormalization group for non-Abelian symmetries. Phys. Rev. B 78, 245109 (2008)

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Acknowledgements

We are grateful to S. Amasha, Y. Oreg, A. Carmi, E. Sela, A. K. Mitchell and M. Heiblum for discussions; H. K. Choi, Y. Chung and J. MacArthur for electronics expertise; M. Heiblum for use of his laboratory during initial device characterization; H. Inoue, N. Ofek, O. Raslin and E. Weisz for fabrication guidance; F. B. Anders, E. Lebanon and the late A. Schiller for their calculations which guided prior experimental work; and M. Stopa for his SETE software for electrostatic quantum dot modelling. The device was fabricated in the Braun Submicron Center at the Weizmann Institute of Science, with final fabrication steps done at Stanford Nano Shared Facilities (SNSF) at Stanford University. This work was supported by the Gordon and Betty Moore Foundation grant no. GBMF3429, the Hungarian research grant OTKA K105149, the Polish National Science Centre project no. DEC-2013/10/E/ST3/00213, EU grant no. CIG-303 689, the National Science Foundation grant no. DMR-0906062, and the US-Israel BSF grant no. 2008149. A.J.K. and L.P. were supported by a Stanford Graduate Fellowship. SETE calculations were run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University. NRG calculations were performed at the Poznań Supercomputing and Networking Center.

Author information

Author notes

    • A. J. Keller

    Present address: Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA.

Affiliations

  1. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA

    • A. J. Keller
    • , L. Peeters
    •  & D. Goldhaber-Gordon
  2. BME-MTA Exotic Quantum Phases “Lendület” Group, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

    • C. P. Moca
    •  & G. Zaránd
  3. Department of Physics, University of Oradea, Oradea 410087, Romania

    • C. P. Moca
  4. Faculty of Physics, Adam Mickiewicz University, Poznań 61-614, Poland

    • I. Weymann
  5. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 96100, Israel

    • D. Mahalu
    •  & V. Umansky

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Contributions

A.J.K., G.Z. and D.G.-G. designed the experiment. A.J.K. and L.P. performed the measurements. 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., L.P., C.P.M., I.W., G.Z. and D.G.-G. analysed the data. A.J.K. designed and fabricated the devices, with e-beam lithography from D.M., using heterostructures grown by V.U. A.J.K. and L.P. wrote the paper with critical review provided by all other authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to D. Goldhaber-Gordon.

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DOI

https://doi.org/10.1038/nature15261

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