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Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research. By studying the Bragg peaks in Fourier transforms of electronic structure images, and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such Bragg-peak Fourier analysis. Exemplary of this challenge is the high temperature superconductor Bi2Sr2CaCu2O8+d for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ~2% (2pi) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unit-cell rotational symmetry breaking at the CuO2 plane. Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for Bragg-peak Fourier analysis of intra-unit-cell symmetry., Comment: Main article + figures, Supplementary Data + Figures; accepted to New Journal of Physics

Replacing a magnetic atom by a spinless atom in a heavy fermion compound generates a quantum state often referred to as a 'Kondo-hole'. No experimental imaging has been achieved of the atomic-scale electronic structure of a Kondo-hole, or of their destructive impact (Lawrence JM, et al. (1996) Kondo hole behavior in Ce0. 97La0. 03Pd3. Phys Rev B 53:12559-12562; Bauer ED, et al. (2011) Electronic inhomogeneity in a Kondo lattice. Proc Natl Acad Sci. 108:6857-6861) on the hybridization process between conduction and localized electrons which generates the heavy fermion state. Here we report visualization of the electronic structure at Kondo-holes created by substituting spinless Thorium atoms for magnetic Uranium atoms in the heavy-fermion system URu2Si2. At each Thorium atom, an electronic bound state is observed. Moreover, surrounding each Thorium atom we find the unusual modulations of hybridization strength recently predicted to occur at Kondo-holes (Figgins J, Morr DK (2011) Defects in heavy-fermion materials: unveiling strong correlations in real space. Phys Rev Lett 107:066401). Then, by introducing the 'hybridization gapmap' technique to heavy fermion studies, we discover intense nanoscale heterogeneity of hybridization due to a combination of the randomness of Kondo-hole sites and the long-range nature of the hybridization oscillations. These observations provide direct insight into both the microscopic processes of heavy-fermion forming hybridization and the macroscopic effects of Kondo-hole doping., Comment: Main Article + Figures, Supporting Information + Figures; PNAS 2011