The Kondo effect arises from the quantum mechanical interplay between the electrons of a host metal and a magnetic impurity and is predicted to result in local charge and spin variations around the magnetic impurity. A cryogenic scanning tunneling microscope was used to spatially resolve the electronic properties of individual magnetic atoms displaying the Kondo effect. Spectroscopic measurements performed on individual cobalt atoms on the surface of gold show an energetically narrow feature that is identified as the Kondo resonance-the predicted response of a Kondo impurity. Unexpected structure in the Kondo resonance is shown to arise from quantum mechanical interference between the d orbital and conduction electron channels for an electron tunneling into a magnetic atom in a metallic host.

Scanning tunneling microscopy is used to image the additional quasi-particle states generated by quantized vortices in the high critical temperature superconductor Bi2Sr2CaCu2O8+delta. They exhibit a copper-oxygen bond-oriented "checkerboard" pattern, with four unit cell (4a0) periodicity and a approximately 30 angstrom decay length. These electronic modulations may be related to the magnetic field-induced, 8a0 periodic, spin density modulations with decay length of approximately 70 angstroms recently discovered in La1.84Sr0.16CuO4. The proposed explanation is a spin density wave localized surrounding each vortex core. General theoretical principles predict that, in the cuprates, a localized spin modulation of wavelength lambda should be associated with a corresponding electronic modulation of wavelength lambda/2, in good agreement with our observations.

Granular superconductivity occurs when microscopic superconducting grains are separated by non-superconducting regions through which they communicate by Josephson tunneling to establish the macroscopic superconducting state 1 . Although crystals of the cuprate high-T c superconductors are not granular in a structural sense, theory indicates that at low hole densities the holes can become concentrated at some locations resulting in hole-rich superconducting domains 2-5 . Granular superconductivity due to Josephson tunneling through 'undoped' regions between such domains would represent a new paradigm for the underdoped cuprates. Here we report studies of the spatial interrelationships between STM tunneling spectra in underdoped Bi 2 Sr 2 CaCu 2 O 8+d . They reveal an apparent spatial segregation of the electronic structure into ~3nm diameter domains (with superconducting characteristics and local energy gap ∆<50 meV) in an electronically distinct background. To explore whether this represents nanoscale segregation of two distinct electronic phases, we employ scattering-resonances at Ni impurity atoms 6 as 'markers' for the local existence of superconductivity [7][8][9] . No Ni-resonances are detected in any regions where ∆>50±2.5 meV. These observations suggest that underdoped Bi 2 Sr 2 CaCu 2 O 8+d is a mixture of two different short-range electronic orders with the long-range characteristics of a granular superconductor.

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In conventional superconductors, magnetic interactions and magnetic impurity atoms are destructive to superconductivity 1 . By contrast, in some unconventional systems, e.g. superfluid 3He and superconducting UGe 2 , superconductivity or superfluidity is actually mediated by magnetic interactions. A magnetic mechanism has also been proposed for high temperature superconductivity (HTSC) in which an electron magnetically polarizes its environment resulting in an attractive pairing-interaction for oppositely polarized spins [2][3][4][5][6] . Since a magnetic impurity atom would apparently not disrupt such a pairing-interaction, it has also been proposed 5,6 that the weaker influences on HTSC of magnetic Ni impurity atoms compared to those of non-magnetic Zn are evidence for a magnetic mechanism. Here we use scanning tunneling microscopy (STM) to determine directly the influence of individual Ni atoms on the electronic structure of Bi 2 Sr 2 CaCu 2 O 8+δ δ δ δ . Two local d-wave impurity-states 7,8 are observed at each Ni. Analysis of their energies surprisingly reveals that the primary quasiparticle scattering effects of Ni atoms are due to non-magnetic interactions. Nonetheless, we also demonstrate that a magnetic moment coexists with unimpaired superconductivity at each Ni site. We discuss the implications of these phenomena, and those at Zn 9 , for the pairing-mechanism.In our studies we use two different Bi 2 Sr 2 Ca(Cu 1-x Ni x ) 2 O 8+δ single crystals, grown by the floating-zone technique. These crystals have x = 0.005 with T c = 83 K and x = 0.002 with T c = 85 K, respectively. The Ni atoms substitute for Cu atoms in the superconducting CuO 2 plane and are believed to be in the Ni

In topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with distinct characteristics. The breaking of crystal symmetry in TCIs is predicted to impart mass to the massless Dirac fermions. Here, we report high-resolution scanning tunneling microscopy studies of a TCI, Pb(1-x)Sn(x)Se that reveal the coexistence of zero-mass Dirac fermions protected by crystal symmetry with massive Dirac fermions consistent with crystal symmetry breaking. In addition, we show two distinct regimes of the Fermi surface topology separated by a Van-Hove singularity at the Lifshitz transition point. Our work paves the way for engineering the Dirac band gap and realizing interaction-driven topological quantum phenomena in TCIs.

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