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Imaging the Fano lattice to ‘hidden order’ transition in URu2Si2

Nature volume 465, pages 570576 (03 June 2010) | Download Citation


Within a Kondo lattice, the strong hybridization between electrons localized in real space (r-space) and those delocalized in momentum-space (k-space) generates exotic electronic states called ‘heavy fermions’. In URu2Si2 these effects begin at temperatures around 55 K but they are suddenly altered by an unidentified electronic phase transition at To = 17.5 K. Whether this is conventional ordering of the k-space states, or a change in the hybridization of the r-space states at each U atom, is unknown. Here we use spectroscopic imaging scanning tunnelling microscopy (SI-STM) to image the evolution of URu2Si2 electronic structure simultaneously in r-space and k-space. Above To, the ‘Fano lattice’ electronic structure predicted for Kondo screening of a magnetic lattice is revealed. Below To, a partial energy gap without any associated density-wave signatures emerges from this Fano lattice. Heavy-quasiparticle interference imaging within this gap reveals its cause as the rapid splitting below To of a light k-space band into two new heavy fermion bands. Thus, the URu2Si2 ‘hidden order’ state emerges directly from the Fano lattice electronic structure and exhibits characteristics, not of a conventional density wave, but of sudden alterations in both the hybridization at each U atom and the associated heavy fermion states.

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  1. 1.

    The Kondo Problem to Heavy Fermions (Cambridge University Press, 1993)

  2. 2.

    Non fermi liquids. Contemp. Phys. 40, 95–115 (1999)

  3. 3.

    Handbook of Magnetism and Advanced Magnetic Materials. Vol. 1 Fundamental Theory (eds Kronmüller, H. & Parkin, S.) 95–148 (John Wiley, 2007)

  4. 4.

    Resistance minimum in dilute magnetic alloys. Prog. Theor. Phys. 32, 37–49 (1964)

  5. 5.

    et al. Tunneling into a single magnetic atom: spectroscopic evidence of the Kondo resonance. Science 280, 567–569 (1998)

  6. 6.

    , & Quantum mirages formed by coherent projection of electronic structure. Nature 403, 512–515 (2000)

  7. 7.

    et al. Kondo effect in single Co adatoms on Cu surfaces. Phys. Rev. Lett. 88, 096804 (2002)

  8. 8.

    Heavy-fermion systems. Rev. Mod. Phys. 56, 755–787 (1984)

  9. 9.

    et al. Classification of strongly correlated f-electron systems. J. Low-Temp. Phys. 99, 267–278 (1995)

  10. 10.

    Superconductivity and magnetism in heavy-fermion compounds. J. Phys. Soc. Jpn 74, 167–177 (2005)

  11. 11.

    , & Theory of heavy fermion systems. Solid State Phys. 41, 1–151 (1988)

  12. 12.

    & Arrested Kondo effect and hidden order in URu2Si2. Nature Phys. 5, 796–799 (2009)

  13. 13.

    , & Electron cotunneling into a Kondo lattice. Phys. Rev. Lett. 10, 206402 (2009)

  14. 14.

    & Differential conductance and quantum interference in Kondo systems. Phys. Rev. Lett. (in the press); preprint at 〈〉 (2010)

  15. 15.

    et al. Partially gapped fermi surface in the heavy-electron superconductor URu2Si2. Phys. Rev. Lett. 56, 185–188 (1986)

  16. 16.

    , & Superconducting and magnetic transitions in the heavy-fermion system URu2Si2. Phys. Rev. Lett. 55, 2727–2730 (1985)

  17. 17.

    et al. Hall effect and resistivity study of the heavy-fermion system URu2Si2. Phys. Rev. B 35, 5375–5378 (1987)

  18. 18.

    et al. Comparative study of the electronic structure of XRu2Si2: probing the Anderson lattice. J. Elec. Spectrosc. 117–118, 347–369 (2001)

  19. 19.

    et al. Far-infrared properties of URu2Si2. Phys. Rev. Lett. 61, 1305–1308 (1988)

  20. 20.

    et al. Hybridization gap in heavy fermion compounds. Phys. Rev. Lett. 86, 684–687 (2001)

  21. 21.

    et al. Point contact spectroscopy of URu2Si2. Phys. Rev. B. 55, 14318–14322 (1997)

  22. 22.

    & Temperature dependence of the antiferromagnetic state in URu2Si2 by point-contact spectroscopy. Phys. Rev. B 49, 15271–15275 (1994)

  23. 23.

    et al. Magnetic excitations and order in the heavy-electron superconductor URu2Si2. Phys. Rev. Lett. 58, 1467–1470 (1987)

  24. 24.

    et al. Gapped Itinerant spin excitations account for missing entropy in the hidden order state of URu2Si2. Nature Phys. 3, 96–99 (2007)

  25. 25.

    et al. Incommensurate spin resonance in URu2Si2. Phys. Rev. B 79, 214413 (2009)

  26. 26.

    et al. Fermi-surface instability at the ‘hidden-order’ transition of URu2Si2. Nature Phys. 5, 637–641 (2009)

  27. 27.

    & Theory of unconventional spin density wave: a possible mechanism of the micromagnetism in U-based heavy fermion compounds. Phys. Rev. Lett. 81, 3723–3726 (1998)

  28. 28.

    & Helicity order: hidden order parameter in URu2Si2. Phys. Rev. Lett. 96, 036405 (2006)

  29. 29.

    et al. Hidden orbital order in the heavy fermion metal URu2Si2. Nature 417, 831–834 (2002)

  30. 30.

    et al. Magnetic excitations in the heavy-fermion superconductor URu2Si2. Phys. Rev. B 43, 12809–12822 (1991)

  31. 31.

    & Singlet magnetism in heavy fermions. Phys. Rev. Lett. 74, 4301–4304 (1995)

  32. 32.

    Crystal field model of the magnetic properties of URu2Si2. Phys. Rev. Lett. 73, 1027–1030 (1994)

  33. 33.

    & Complex Landau Ginzburg theory of the hidden order of URu2Si2. Europhys. Lett. 89, 57006 (2010)

  34. 34.

    , & Why the hidden order in URu2Si2 is still hidden—one simple answer. J. Phys. Soc. Jpn 79, 033705 (2010)

  35. 35.

    Density Waves in Solids (Perseus Publishing, 1994)

  36. 36.

    , & Imaging standing waves in a two-dimensional electron gas. Nature 363, 524–527 (1993)

  37. 37.

    & Quasiparticle scattering interference in high-temperature superconductors. Phys. Rev. B 67, 020511 (2003)

  38. 38.

    et al. Imaging quasiparticle interference in BiSr2Ca2CuO8+δ. Science 297, 1148–1151 (2002)

  39. 39.

    et al. Relating atomic-scale electronic phenomena to wave-like quasiparticle states in superconducting Bi2Sr2CaCu2O8+δ. Nature 422, 592–596 (2003)

  40. 40.

    et al. Coherence factors in a high-Tc cuprate probed by quasi-particle scattering off vortices. Science 323, 923–926 (2009)

  41. 41.

    How cooper pairs vanish approaching the Mott insulator in BiSr2Ca2CuO8+δ. Nature 454, 1072–1078 (2008)

  42. 42.

    et al. Imaging nanoscale Fermi-surface variations in an inhomogeneous superconductor. Nature Phys. 5, 213–216 (2009)

  43. 43.

    et al. Heavy d-electron quasiparticle interference and real-space electronic structure of Sr3Ru2O7. Nature Phys. 5, 800–804 (2009)

  44. 44.

    , & Friedel oscillations and the Kondo screening cloud. Phys. Rev. B 77, 180404 (2008)

  45. 45.

    & Defects in heavy-fermion materials: unveiling strong correlations in real space. Preprint at 〈〉 (2010)

  46. 46.

    et al. Th-doped URu2Si2: influence of Kondo holes on coexisting superconductivity and magnetism. Physica B 179, 208–214 (1992)

  47. 47.

    et al. Thorium dilution effects of the heavy electron compound URu2Si2. Physica B 312, 498–500 (2002)

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We acknowledge and thank E. Abrahams, M. Aronson, D. Bonn, W. Buyers, A. Chantis, M. Crommie, P. Coleman, D. M. Eigler, M. Graf, A. Greene, K. Haule, C. Hooley, G. Kotliar, D.-H. Lee, A. J. Leggett, B. Maple, F. Steglich, V. Madhavan, A. P. Mackenzie, S. Sachdev, A. Schofield, T. Senthil and D. Pines for discussions and communications. These studies were supported by the US Department of Energy, Office of Basic Energy Sciences, under Award Number DE-2009-BNL-PM015. Research at McMaster University was supported by NSERC and CIFAR. Research at Los Alamos was supported in part by the Center for Integrated Nanotechnology, a US Department of Energy Office of Basic Energy Sciences user facility, under contract DE-AC52-06NA25396, by LDRD funds and by UCOP TR01. P.W. acknowledges support from the Humboldt Foundation, F.M. from the German Academic Exchange Service, and A.R.S. from the US Army Research Office. J.C.D. gratefully acknowledges the hospitality and support of the Physics and Astronomy Department at the University of British Columbia.

Author information


  1. Laboratory for Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA

    • A. R. Schmidt
    • , M. H. Hamidian
    • , P. Wahl
    • , F. Meier
    •  & J. C. Davis
  2. Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA

    • A. R. Schmidt
    • , M. H. Hamidian
    •  & J. C. Davis
  3. Max-Planck-Institut für Festkörperforschung, Heisenbergstraße1, D-70569 Stuttgart, Germany

    • P. Wahl
  4. Theory Division and Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

    • A. V. Balatsky
  5. Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, L85 4M1, Canada

    • J. D. Garrett
  6. Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada

    • T. J. Williams
    •  & G. M. Luke
  7. Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1Z8, Canada

    • G. M. Luke
  8. School of Physics and Astronomy, University of St Andrews, St Andrews, Fife KY16 9SS, UK

    • J. C. Davis
  9. Department of Physics and Astronomy, University of British Columbia, Vancouver, V6T 1Z1, Canada

    • J. C. Davis


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A.R.S., M.H.H., P.W. and F.M. performed the SI-STM measurements and data analysis. J.D.G, T.J.W. and G.M.L. synthesized and characterized the materials. A.V.B. provided the theoretical framework. J.C.D. wrote the manuscript and supervised the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to J. C. Davis.

Supplementary information

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  1. 1.

    Supplementary Information

    This file contains Supplementary Notes (I)-(IX), Supplementary Figures S1-S9 with legends and References.


  1. 1.

    Supplementary Video 1

    This movie shows the Fourier transform of the real space conductance maps of Th-doped URu2Si2 in the heavy fermion paramagnetic phase at a temperature of 19K. The patterns are due to quasiparticle interference. The red diamonds in the corners mark the locations of the U atom reciprocal lattice vectors.

  2. 2.

    Supplementary Video 2

    This movie shows the Fourier transform of the real space conductance maps of Th-doped URu2Si2 in the hidden order phase at a temperature of 1.9K. The red diamonds in the corners mark the locations of the U atom reciprocal lattice vectors. The patterns are due to quasiparticle interference. The two dimensional patterns are seen to become highly separated from the patterns seen at 19K for biases -3mV to 3mV.

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