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

Abstract

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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Figure 1: A Kondo lattice model and its resulting band structure.
Figure 2: Imaging the Fano lattice in URu2Si2.
Figure 3: Evolution of DOS( E ) upon entering the hidden-order phase.
Figure 4: Energy dependence of heavy f -electron quasiparticle interference.
Figure 5: Emergence of the two new heavy bands below the hidden-order transition.

References

  1. 1

    Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge University Press, 1993)

    Book  Google Scholar 

  2. 2

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

    ADS  CAS  Article  Google Scholar 

  3. 3

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

    Google Scholar 

  4. 4

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

    ADS  CAS  Article  Google Scholar 

  5. 5

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

    ADS  CAS  Article  Google Scholar 

  6. 6

    Manoharan, H. C., Luta, C. P. & Eigler, D. M. Quantum mirages formed by coherent projection of electronic structure. Nature 403, 512–515 (2000)

    ADS  CAS  Article  Google Scholar 

  7. 7

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

    ADS  Article  Google Scholar 

  8. 8

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

    ADS  CAS  Article  Google Scholar 

  9. 9

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

    ADS  CAS  Article  Google Scholar 

  10. 10

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

    ADS  CAS  Article  Google Scholar 

  11. 11

    Fulde, P., Keller, J. & Zwicknagl, G. Theory of heavy fermion systems. Solid State Phys. 41, 1–151 (1988)

    CAS  Article  Google Scholar 

  12. 12

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

    ADS  CAS  Article  Google Scholar 

  13. 13

    Maltseva, M., Dzero, M. & Coleman, P. Electron cotunneling into a Kondo lattice. Phys. Rev. Lett. 10, 206402 (2009)

    ADS  Article  Google Scholar 

  14. 14

    Figgins, J. & Morr, D. K. Differential conductance and quantum interference in Kondo systems. Phys. Rev. Lett. (in the press); preprint at 〈http://arxiv.org/abs/1001.4530v1〉 (2010)

  15. 15

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

    ADS  CAS  Article  Google Scholar 

  16. 16

    Palstra, T. T. M., Menovsky, A. A. & Mydosh, J. A. Superconducting and magnetic transitions in the heavy-fermion system URu2Si2 . Phys. Rev. Lett. 55, 2727–2730 (1985)

    ADS  CAS  Article  Google Scholar 

  17. 17

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

    ADS  CAS  Article  Google Scholar 

  18. 18

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

    Article  Google Scholar 

  19. 19

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

    ADS  CAS  Article  Google Scholar 

  20. 20

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

    ADS  CAS  Article  Google Scholar 

  21. 21

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

    ADS  CAS  Article  Google Scholar 

  22. 22

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

    ADS  CAS  Article  Google Scholar 

  23. 23

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

    ADS  CAS  Article  Google Scholar 

  24. 24

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

    ADS  CAS  Article  Google Scholar 

  25. 25

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

    ADS  Article  Google Scholar 

  26. 26

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

    ADS  CAS  Article  Google Scholar 

  27. 27

    Ikeda, H. & Ohashi, Y. 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)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Varma, C. M. & Lijun, Z. Helicity order: hidden order parameter in URu2Si2 . Phys. Rev. Lett. 96, 036405 (2006)

    ADS  CAS  Article  Google Scholar 

  29. 29

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

    ADS  CAS  Article  Google Scholar 

  30. 30

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

    ADS  CAS  Article  Google Scholar 

  31. 31

    Barzykin, V. & Gor’kov, L. P. Singlet magnetism in heavy fermions. Phys. Rev. Lett. 74, 4301–4304 (1995)

    ADS  CAS  Article  Google Scholar 

  32. 32

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

    ADS  CAS  Article  Google Scholar 

  33. 33

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

    ADS  Article  Google Scholar 

  34. 34

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

    ADS  Article  Google Scholar 

  35. 35

    Grüner, G. Density Waves in Solids (Perseus Publishing, 1994)

    Google Scholar 

  36. 36

    Crommie, M. F., Lutz, C. P. & Eigler, D. M. Imaging standing waves in a two-dimensional electron gas. Nature 363, 524–527 (1993)

    ADS  CAS  Article  Google Scholar 

  37. 37

    Wang, Q. H. & Lee, D. H. Quasiparticle scattering interference in high-temperature superconductors. Phys. Rev. B 67, 020511 (2003)

    ADS  Article  Google Scholar 

  38. 38

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

    ADS  CAS  Article  Google Scholar 

  39. 39

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

    ADS  CAS  Article  Google Scholar 

  40. 40

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

    ADS  CAS  Article  Google Scholar 

  41. 41

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

    ADS  CAS  Article  Google Scholar 

  42. 42

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

    ADS  CAS  Article  Google Scholar 

  43. 43

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

    ADS  CAS  Article  Google Scholar 

  44. 44

    Affleck, I., Borda, L. & Saleur, H. Friedel oscillations and the Kondo screening cloud. Phys. Rev. B 77, 180404 (2008)

    ADS  Article  Google Scholar 

  45. 45

    Figgins, J. & Morr, D. K. Defects in heavy-fermion materials: unveiling strong correlations in real space. Preprint at 〈http://arxiv.org/abs/1001.3875〉 (2010)

  46. 46

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

    Article  Google Scholar 

  47. 47

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

    ADS  Article  Google Scholar 

Download references

Acknowledgements

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.

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Contributions

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.

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Correspondence to J. C. Davis.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Notes (I)-(IX), Supplementary Figures S1-S9 with legends and References. (PDF 1922 kb)

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. (MPG 2411 kb)

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. (MPG 4925 kb)

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Schmidt, A., Hamidian, M., Wahl, P. et al. Imaging the Fano lattice to ‘hidden order’ transition in URu2Si2. Nature 465, 570–576 (2010). https://doi.org/10.1038/nature09073

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