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 the RXS experiments remains theoretically challenging due to the complex
ity of the RXS cross-section. Central to this debate is the recent proposal that impurity-induced Friedel oscillations, akin to quasiparticle interference signals observed with the scanning tunneling microscope (STM), can lead to scattering peaks in the RXS experiments. The possibility that quasiparticle 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. Here, we test these ideas by combining RXS and STM measurements of the heavy fermion compound CeMIn$_5$ (M = Co, Rh). Temperature and doping dependent RXS measurements at the Ce-M$_4$ 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 quasiparticle interference signal in the STM measurements, indicating that quasiparticle 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.
In cuprate high-temperature superconductors, an antiferromagnetic Mott insulating state can be destabilized toward unconventional superconductivity by either hole- or electron-doping. In addition to these two electronic phases there is now a copious
amount of evidence that supports the presence of a charge ordering (CO) instability competing with superconductivity inside the pseudogap state of the hole-doped (p-type) cuprates, but so far there has been no evidence of a similar CO in their electron-doped (n-type) counterparts. Here we report resonant x-ray scattering (RXS) measurements which demonstrate the presence of charge ordering in the n-type cuprate Nd2-xCexCuO4 near optimal doping. Remarkably we find that the CO in Nd2-xCexCuO4 occurs with similar periodicity, and along the same direction, as the CO in p-type cuprates. However, in contrast to the latter, the CO onset in Nd2-xCexCuO4 is higher than the pseudogap temperature, and is actually in the same temperature range where antiferromagnetic fluctuations are first detected -- thereby showing that CO and antiferromagnetic fluctuations are likely coupled in n-type cuprates. Overall our discovery uncovers a missing piece of the cuprate phase diagram and opens a parallel path to the study of CO and its relationship to other phenomena, such as antiferromagnetism (AF) and high-temperature superconductivity.
Besides superconductivity, copper-oxide high temperature superconductors are susceptible to other types of ordering. We use scanning tunneling microscopy and resonant elastic x-ray scattering measurements to establish the formation of charge ordering
in the high-temperature superconductor Bi2Sr2CaCu2O8+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 observe this charge ordering to leave a distinct electron-hole asymmetric signature (and a broad resonance centered at +20 meV) in spectroscopic measurements, thereby indicating that it is likely related to the organization of holes in a doped Mott insulator.
Understanding the origin of superconductivity in strongly correlated electron systems continues to be at the forefront of unsolved problems in all of physics. Among the heavy f-electron systems, CeCoIn5 is one of the most fascinating, as it shares ma
ny of the characteristics of correlated d-electron high-Tc cuprate and pnictide superconductors, including the competition between antiferromagnetism and superconductivity. While there has been evidence for unconventional pairing in this compound, high-resolution spectroscopic measurements of the superconducting state have been lacking. Previously, we have used high-resolution scanning tunneling microscopy techniques to visualize the emergence of heavy-fermion excitations in CeCoIn5 and demonstrate the composite nature of these excitations well above Tc. Here we extend these techniques to much lower temperatures to investigate how superconductivity develops within a strongly correlated band of composite excitations. We find the spectrum of heavy excitations to be strongly modified just prior to the onset of superconductivity by a suppression of the spectral weight near the Fermi energy, reminiscent of the pseudogap state in the cuprates. By measuring the response of superconductivity to various perturbations, through both quasiparticle interference and local pair-breaking experiments, we demonstrate the nodal d-wave character of superconducting pairing in CeCoIn5.
Electronic nematic phases have been proposed to occur in various correlated electron systems and were recently claimed to have been detected in scanning tunneling microscopy (STM) conductance maps of the pseudogap states of the cuprate high-temperatu
re superconductor Bi2Sr2CaCu2O8+x (Bi-2212). We investigate the influence of anisotropic STM tip structures on such measurements and establish, with a model calculation, the presence of a tunneling interference effect within an STM junction that induces energy-dependent symmetry-breaking features in the conductance maps. We experimentally confirm this phenomenon on different correlated electron systems, including measurements in the pseudogap state of Bi-2212, showing that the apparent nematic behavior of the imaged crystal lattice is likely not due to nematic order but is related to how a realistic STM tip probes the band structure of a material. We further establish that this interference effect can be used as a sensitive probe of changes in the momentum structure of the samples quasiparticles as a function of energy.
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 th
e 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.
Recently we have used spectroscopic mapping with the scanning tunneling microscope to probe modulations of the electronic density of states in single crystals of the high temperature superconductor Bi2Sr2CaCu2O8+d (Bi-2212) as a function of temperatu
re [C. V. Parker et al., Nature (London) 468, 677 (2010)]. These measurements showed Cu-O bond-oriented modulations that form below the pseudogap temperature with a temperature-dependent energy dispersion displaying different behaviors in the superconducting and pseudogap states. Here we demonstrate that quasiparticle scattering off impurities does not capture the experimentally observed energy- and temperature-dependence of these modulations. Instead, a model of scattering of quasiparticles from short-range stripe order, with periodicity near four lattice constants (4a), reproduces the experimentally observed energy dispersion of the bond-oriented modulations and its temperature dependence across the superconducting critical temperature, Tc. The present study confirms the existence of short-range stripe order in Bi-2212.
Doped Mott insulators have been shown to 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 transforms into a high temperature superconduct
or with sufficient doping or by reducing the temperature. A long standing question has been the interplay between pseudogap, which is generic to all hole-doped cuprates, and stripes, whose static form occurs in only one family of cuprates over a narrow range of the phase diagram. Here we examine the spatial reorganization of electronic states with the onset of the pseudogap state at T* in the high-temperature superconductor Bi2Sr2CaCu2O8+x using spectroscopic mapping with the scanning tunneling microscope (STM). 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 CuO2 planes is close to 1/8 (per Cu). While demonstrating that the fluctuating stripes emerge with the onset of the pseudogap state and occur over a large part of the cuprate phase diagram, our experiments indicate that they are a consequence of pseudogap behavior rather than its cause.
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 (STM) to examine the novel electronic states that
emerge from the uranium f states in URu2Si2. 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, URu2Si2 is known to undergo a 2nd 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.
