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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.

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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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Authors

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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