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.
Figures at a glance
Figure 1: A Kondo lattice model and its resulting band structure. 
a, A schematic representation of the screening of a localized spin-half state (red) by delocalized k-space electrons (green) caused by the Kondo effect1, 2, 3, 4, 5. b, A typical Fano tunnelling-conductance spectrum5 expected near the electronic many-body state depicted in a. c, A schematic representation of the T ≈ 0 band structure expected of a Kondo lattice as in equation (2), with the light hole-like band at high temperature depicted by a dashed line. The approximate hybridization energy range is shown by horizontal arrows.
Figure 2: Imaging the Fano lattice in URu2Si2. 
a, A typical topographic image of the Si-terminated surface of URu2Si2. The Si site is marked with a cross and the U site with an X. Data were acquired at −60 mV and 2 GΩ junction resistance. b, A typical spatially averaged Fano-like <g(E)> spectrum detected on all Si-terminated surfaces of URu2Si2 at T < 20 K. The inset shows the layered structure of the crystal with the U-terminated surface; the Si-terminated surface is two atomic layers below with each Si at the middle site between four U atoms. c, Image of the many-body state energy ε0(r) extracted from fitting the spatially resolved Fano spectrum according to equation (1); the FOV is indicated by the yellow box in a. U atoms are designated by an X and the maximum in ε0 always occurs at these sites. d, Image of the hybridization width Γ(r) extracted from fitting the spatially resolved Fano spectrum according to equation (1); the FOV is the same as in c. The minimum in Γ occurs at the U sites. e, Image of the ratio of electron tunnelling probability ζ(r) extracted from fitting the spatially resolved Fano spectrum according to equation (1); the FOV is the same as in c and d. The maximum in ζ occurs at the U sites.
Figure 3: Evolution of DOS(E) upon entering the hidden-order phase. 
a, Topographic image of U-terminated surface with the temperature dependence of its spatially averaged spectra <g(E)> in the inset. Each of these spectra is shifted vertically by 5 nS for clarity. Blue data are within 1 K of To for 1% Th-doped samples. The image was taken at −10 mV and 2.5 MΩ junction resistance. b, Temperature dependence of DOS(E) modifications due to the appearance of the hidden order at the U-terminated surfaces. Each spectrum is derived by subtracting the spectrum for T > To (and shifted vertically for clarity). The DOS(E) changes are limited to approximately ±5 meV. c, Topographic image of Si-terminated surface with the temperature dependence of its spatially averaged spectra <g(E)> in the inset. Each of these spectra is shifted vertically by 5 nS for clarity. The image was taken at 150 mV and 3 GΩ junction resistance. d, Temperature dependence of DOS(E) modifications due to the appearance of the hidden order at the Si-terminated surfaces. Each spectrum is derived by subtracting the fit to a Fano spectrum (equation (1)), which excludes data points in the range −7.75 mV to 6.75 mV. The DOS(E) changes are again limited to approximately ±5 meV.
Figure 4: Energy dependence of heavy f-electron quasiparticle interference. 
a–f, Atomically resolved g(r, E) for six energies measured at the U-terminated surface. Extremely rapid changes in the interference patterns occur within an energy range of only a few millielectronvolts. Data were acquired at –6 mV and 25 MΩ setpoint junction resistance. g–l, Fourier transforms g(q, E) of the g(r, E) in a–f. The associated g(q, E) movie is shown in the Supplementary Information. The length of half-reciprocal unit-cell vectors are shown as dots at the edge of each image. Starting at energies below EF (g), the predominant QPI wavevectors diminish very rapidly until i; upon crossing a few millielectronvolts above EF, they jump to a significantly larger value and rotate through 45°. Then they again diminish in radius with increasing energy in j, k and l. This evolution is not consistent with a fixed Q* conventional density wave state but is consistent with an avoided crossing between a light band and a very heavy band.
Figure 5: Emergence of the two new heavy bands below the hidden-order transition. 
a, Dispersion of the primary QPI wavevector for T > To along the (0, 1) direction (see Fig. 4g). A single light hole-like band crosses EF. b, Dispersion of the primary QPI wavevector for T > To along the (1, 1) direction (see Fig. 4g). A single light hole-like band crosses EF. c, Dispersion of the primary QPI wavevector for T ≈ 5.9 K along the (0, 1) direction (see Fig. 4g). Two heavy bands have evolved from the light band and become well segregated in k-space within the hybridization gap. d, Dispersion of the primary QPI wavevector for T ≈ 5.9 K along the (1, 1) direction (see Fig. 4g). Two heavy bands have evolved from the light band and are again segregated in k-space within the hybridization gap.
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