Visualizing heavy fermions emerging in a quantum critical Kondo lattice.

In solids containing elements with f orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are fundamental to the appearance of unconventional superconductivity and non-Fermi-liquid behaviour observed in actinide- and lanthanide-based compounds. Here we use spectroscopic mapping with the scanning tunnelling microscope to detect the emergence of heavy excitations with lowering of temperature in a prototypical family of cerium-based heavy-fermion compounds. We demonstrate the sensitivity of the tunnelling process to the composite nature of these heavy quasiparticles, which arises from quantum entanglement of itinerant conduction and f electrons. Scattering and interference of the composite quasiparticles is used to resolve their energy-momentum structure and to extract their mass enhancement, which develops with decreasing temperature. The lifetime of the emergent heavy quasiparticles reveals signatures of enhanced scattering and their spectral lineshape shows evidence of energy-temperature scaling. These findings demonstrate that proximity to a quantum critical point results in critical damping of the emergent heavy excitation of our Kondo lattice system.

Fluctuating stripes at the onset of the pseudogap in the high-T(c) superconductor Bi(2)Sr(2)CaCu(2)O(8+x).

Doped Mott insulators have a strong propensity to form patterns of holes and spins often referred to as stripes. In copper oxides, doping also gives rise to the pseudogap state, which can be transformed into a high-temperature superconducting state with sufficient doping or by reducing the temperature. A long-standing issue has been the interplay between the pseudogap, which is generic to all hole-doped copper oxide superconductors, and stripes, whose static form occurs in only one family of copper oxides over a narrow range of the phase diagram. Here we report observations of the spatial reorganization of electronic states with the onset of the pseudogap state in the high-temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+x), using spectroscopic mapping with a scanning tunnelling microscope. We find that the onset of the pseudogap phase coincides with the appearance of electronic patterns that have the predicted characteristics of fluctuating stripes. As expected, the stripe patterns are strongest when the hole concentration in the CuO(2) planes is close to 1/8 (per copper atom). Although they demonstrate that the fluctuating stripes emerge with the onset of the pseudogap state and occur over a large part of the phase diagram, our experiments indicate that the stripes are a consequence of pseudogap behaviour rather than its cause.

Visualizing the formation of the Kondo lattice and the hidden order in URu(2)Si(2).

Heavy electronic states originating from the f atomic orbitals underlie a rich variety of quantum phases of matter. We use atomic scale imaging and spectroscopy with the scanning tunneling microscope to examine the novel electronic states that emerge from the uranium f states in URu(2)Si(2). We find that, as the temperature is lowered, partial screening of the f electrons' spins gives rise to a spatially modulated Kondo-Fano resonance that is maximal between the surface U atoms. At T = 17.5 K, URu(2)Si(2) is known to undergo a second-order phase transition from the Kondo lattice state into a phase with a hidden order parameter. From tunneling spectroscopy, we identify a spatially modulated, bias-asymmetric energy gap with a mean-field temperature dependence that develops in the hidden order state. Spectroscopic imaging further reveals a spatial correlation between the hidden order gap and the Kondo resonance, suggesting that the two phenomena involve the same electronic states.

Inhomogeneous Kondo-lattice in geometrically frustrated Pr2Ir2O7.

Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long-range magnetic order in the family of pyrochlore iridates. As a consequence, Pr2Ir2O7 lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits an array of complex phenomena including the Kondo effect, biquadratic band structure, and metallic spin liquid. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning, density functional theory and theoretical modeling, we probe the local electronic states in Pr2Ir2O7 and find an electronic phase separation. Nanoscale regions with a well-defined Kondo resonance are interweaved with a non-magnetic metallic phase with Kondo-destruction. These spatial nanoscale patterns display a fractal geometry with power-law behavior extended over two decades, consistent with being in proximity to a critical point. Our discovery reveals a nanoscale tuning route, viz. using a spatial variation of the electronic potential as a means of adjusting the balance between Kondo entanglement and geometric frustration.

Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+ Y Te Using a Spin-polarized Scanning Tunneling Microscope.

The quest to understand correlated electronic systems has pushed the frontiers of experimental measurements toward the development of new experimental techniques and methodologies. Here we use a novel home-built uniaxial-strain device integrated into our variable temperature scanning tunneling microscope that enables us to controllably manipulate in-plane uniaxial strain in samples and probe their electronic response at the atomic scale. Using scanning tunneling microscopy (STM) with spin-polarization techniques, we visualize antiferromagnetic (AFM) domains and their atomic structure in Fe1+yTe samples, the parent compound of iron-based superconductors, and demonstrate how these domains respond to applied uniaxial strain. We observe the bidirectional AFM domains in the unstrained sample, with an average domain size of ~50-150 nm, to transition into a single unidirectional domain under applied uniaxial strain. The findings presented here open a new direction to utilize a valuable tuning parameter in STM, as well as other spectroscopic techniques, both for tuning the electronic properties as for inducing symmetry breaking in quantum material systems.

Orbital-selective Kondo lattice and enigmatic f electrons emerging from inside the antiferromagnetic phase of a heavy fermion.

Novel electronic phenomena frequently form in heavy-fermions because of the mutual localized and itinerant nature of f-electrons. On the magnetically ordered side of the heavy-fermion phase diagram, f-moments are expected to be localized and decoupled from the Fermi surface. It remains ambiguous whether Kondo lattice can develop inside the magnetically ordered phase. Using spectroscopic imaging with scanning tunneling microscope, complemented by neutron scattering, x-ray absorption spectroscopy, and dynamical mean field theory, we probe the electronic states in antiferromagnetic USb2. We visualize a large gap in the antiferromagnetic phase within which Kondo hybridization develops below ~80 K. Our calculations indicate the antiferromagnetism and Kondo lattice to reside predominantly on different f-orbitals, promoting orbital selectivity as a new conception into how these phenomena coexist in heavy-fermions. Finally, at 45 K, we find a novel first order-like transition through abrupt emergence of nontrivial 5f-electronic states that may resemble the "hidden-order" phase of URu2Si2.

High temperature singlet-based magnetism from Hund's rule correlations.

Uranium compounds can manifest a wide range of fascinating many-body phenomena, and are often thought to be poised at a crossover between localized and itinerant regimes for 5f electrons. The antiferromagnetic dipnictide USb2 has been of recent interest due to the discovery of rich proximate phase diagrams and unusual quantum coherence phenomena. Here, linear-dichroic X-ray absorption and elastic neutron scattering are used to characterize electronic symmetries on uranium in USb2 and isostructural UBi2. Of these two materials, only USb2 is found to enable strong Hund's rule alignment of local magnetic degrees of freedom, and to undergo distinctive changes in local atomic multiplet symmetry across the magnetic phase transition. Theoretical analysis reveals that these and other anomalous properties of the material may be understood by attributing it as the first known high temperature realization of a singlet ground state magnet, in which magnetism occurs through a process that resembles exciton condensation.

Visualizing heavy fermion confinement and Pauli-limited superconductivity in layered CeCoIn5.

Layered material structures play a key role in enhancing electron-electron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasi-two-dimensional electronic properties of such compounds are often inferred indirectly through examination of bulk properties. Here we use scanning tunneling microscopy to directly probe in cross-section the quasi-two-dimensional electronic states of the heavy fermion superconductor CeCoIn5. Our measurements reveal the strong confined nature of quasiparticles, anisotropy of tunneling characteristics, and layer-by-layer modulated behavior of the precursor pseudogap gap phase. In the interlayer coupled superconducting state, the orientation of line defects relative to the d-wave order parameter determines whether in-gap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical in-plane magnetic field, consistent with a Pauli-limited first-order phase transition into a pseudogap phase.

Quasi-particle interference of heavy fermions in resonant x-ray scattering.

Resonant x-ray scattering (RXS) has recently become an increasingly important tool for the study of ordering phenomena in correlated electron systems. Yet, the interpretation of RXS experiments remains theoretically challenging because of the complexity of the RXS cross section. Central to this debate is the recent proposal that impurity-induced Friedel oscillations, akin to quasi-particle interference signals observed with a scanning tunneling microscope (STM), can lead to scattering peaks in RXS experiments. The possibility that quasi-particle properties can be probed in RXS measurements opens up a new avenue to study the bulk band structure of materials with the orbital and element selectivity provided by RXS. We test these ideas by combining RXS and STM measurements of the heavy fermion compound CeMIn5 (M = Co, Rh). Temperature- and doping-dependent RXS measurements at the Ce-M4 edge show a broad scattering enhancement that correlates with the appearance of heavy f-electron bands in these compounds. The scattering enhancement is consistent with the measured quasi-particle interference signal in the STM measurements, indicating that the quasi-particle interference can be probed through the momentum distribution of RXS signals. Overall, our experiments demonstrate new opportunities for studies of correlated electronic systems using the RXS technique.

Ubiquitous interplay between charge ordering and high-temperature superconductivity in cuprates.

Besides superconductivity, copper-oxide high-temperature superconductors are susceptible to other types of ordering. We used scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering in the high-temperature superconductor Bi2Sr2CaCu2O(8+x). Depending on the hole concentration, the charge ordering in this system occurs with the same period as those found in Y-based or La-based cuprates and displays the analogous competition with superconductivity. These results indicate the similarity of charge organization competing with superconductivity across different families of cuprates. We observed this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 milli-electron volts) in spectroscopic measurements, indicating that it is likely related to the organization of holes in a doped Mott insulator.