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We conducted a comparative study of the rare-earth infinite-layer nickelates films, RNiO2 (R = La, Pr, and Nd) using resonant inelastic X-ray scattering (RIXS). We found that the gross features of the orbital configurations are essentially the same, with minor variations in the detailed hybridization. For low-energy excitations, we unambiguously confirm the presence of damped magnetic excitations in all three compounds. By fitting to a linear spin-wave theory, comparable spin exchange coupling strengths and damping coefficients are extracted, indicating a universal magnetic structure in the infinite-layer nickelates. Interestingly, while signatures of a charge order are observed in LaNiO2 in the quasi-elastic region of the RIXS spectrum, it is absent in NdNiO2 and PrNiO2. This prompts further investigation into the universality and the origins of charge order within the infinite-layer inickelates., Comment: 8 figures. Accepted by Physical Review B

Low-valence nickelates $-$ including infinite-layer (IL) and trilayer (TL) compounds $-$ are longstanding candidates for mimicking the high-temperature superconductivity of cuprates. A recent breakthrough in the field came with the discovery of superconductivity in hole-doped IL nickelates. Yet, the degree of similarity between low-valence nickelates and cuprates is the subject of a profound debate for which soft x-ray spectroscopy experiments at the Ni $L$- and O $K$-edge provided critical input. In this review, we will discuss the essential elements of the electronic structure of low-valance nickelates revealed by x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS). Furthermore, we will review magnetic excitations observed in the RIXS spectra of IL and TL nickelates, which exhibit characteristics that are partly reminiscent of those of cuprates., Comment: 11 pages, 2 figures, submitted to the Condensed Matter Physics section in Frontiers in Physics for the research topic "Advances in Superconducting Infinite-Layer and Related Nickelates"

The discovery of superconductivity in infinite-layer nickelates brings us tantalizingly close to a new material class that mirrors the cuprate superconductors. Here, we report on magnetic excitations in these nickelates, measured using resonant inelastic x-ray scattering (RIXS) at the Ni L3-edge, to shed light on the material complexity and microscopic physics. Undoped NdNiO2 possesses a branch of dispersive excitations with a bandwidth of approximately 200 meV, reminiscent of strongly-coupled, antiferromagnetically aligned spins on a square lattice, despite a lack of evidence for long range magnetic order. The significant damping of these modes indicates the importance of coupling to rare-earth itinerant electrons. Upon doping, the spectral weight and energy decrease slightly, while the modes become overdamped. Our results highlight the role of Mottness in infinite-layer nickelates., Comment: This is the initially submitted version before revising for reviewers' comments. The peer-reviewed version has been accepted at Science and will be published soon

The recent discovery of superconductivity in Nd$_{1-x}$Sr$_{x}$NiO$_2$ has drawn significant attention in the field. A key open question regards the evolution of the electronic structure with respect to hole doping. Here, we exploit x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) to probe the doping dependent electronic structure of the NiO$_2$ planes. Upon doping, a higher energy feature in Ni $L_3$ edge XAS develops in addition to the main absorption peak. By comparing our data to atomic multiplet calculations including $D_{4h}$ crystal field, the doping induced feature is consistent with a $d^8$ spin singlet state, in which doped holes reside in the $d_{x^2-y^2}$ orbitals, similar to doped single band Hubbard models. This is further supported by orbital excitations observed in RIXS spectra, which soften upon doping, corroborating with Fermi level shift associated with increasing holes in the $d_{x^2-y^2}$ orbital., Comment: 6 pages, 4 figures. Supplemental material included

Copper-oxide high TC superconductors possess a number of exotic orders co-existing with or proximal to superconductivity, whose quantum fluctuations may account for the unusual behaviors of the normal state, even affecting superconductivity. Yet, spectroscopic evidence about such quantum fluctuations remains elusive. Here, we reveal spectroscopic fingerprints for such fluctuations associated with a charge order (CO) in nearly optimally-doped Bi2Sr2CaCu2O8+d, using resonant inelastic x-ray scattering (RIXS). In the superconducting state, while the quasi-elastic CO signal decreases with temperature, the interplay between CO fluctuations and bond-stretching phonons in the form of a Fano-like interference paradoxically increases, incompatible with expectations for competing orders. Invoking general principles, we argue that this behavior reflects the properties of a dissipative system near an order-disorder quantum critical point, where the dissipation varies with the opening of the pseudogap and superconducting gap at low temperatures, leading to the proliferation of quantum critical fluctuations which melt CO., Comment: 24 pages, Supplementary Information included. This is the original submitted manuscript

In the mixed-valence manganites, a near-infrared laser typically melts the orbital and spin order simultaneously, corresponding to the photoinduced $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ excitations in the Mott-Hubbard bands of manganese. Here, we use ultrafast methods -- both femtosecond resonant x-ray diffraction and optical reflectivity -- to demonstrate that the orbital response in the layered manganite Nd$_{1-x}$Sr$_{1+x}$MnO$_{4}$ ($\it{x}$ = 2/3) does not follow this scheme. At the photoexcitation saturation fluence, the orbital order is only diminished by a few percent in the transient state. Instead of the typical $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ transition, a near-infrared pump in this compound promotes a fundamentally distinct mechanism of charge transfer, the $d^{0}$ $ \xrightarrow{}$ $d^{1}L$, where $\it{L}$ denotes a hole in the oxygen band. This novel finding may pave a new avenue for selectively manipulating specific types of order in complex materials of this class.

The search for oxide materials with physical properties similar to the cuprate high Tc superconductors, but based on alternative transition metals such as nickel, has grown and evolved over time. The recent discovery of superconductivity in doped infinite-layer nickelates RNiO2 (R = rare-earth element) further strengthens these efforts.With a crystal structure similar to the infinite-layer cuprates - transition metal oxide layers separated by a rare-earth spacer layer - formal valence counting suggests that these materials have monovalent Ni1+ cations with the same 3d electron count as Cu2+ in the cuprates. Here, we use x-ray spectroscopy in concert with density functional theory to show that the electronic structure of RNiO2 (R = La, Nd), while similar to the cuprates, includes significant distinctions. Unlike cuprates with insulating spacer layers between the CuO2 planes, the rare-earth spacer layer in the infinite-layer nickelate supports a weakly-interacting three-dimensional 5d metallic state. This three-dimensional metallic state hybridizes with a quasi-two-dimensional, strongly correlated state with 3dx2-y2 symmetry in the NiO2 layers. Thus, the infinite-layer nickelate can be regarded as a sibling of the rare earth intermetallics, well-known for heavy Fermion behavior, where the NiO2 correlated layers play an analogous role to the 4f states in rare-earth heavy Fermion compounds. This unique Kondo- or Anderson-lattice-like "oxide-intermetallic" replaces the Mott insulator as the reference state from which superconductivity emerges upon doping., Comment: 28 pages, 5 figures

High temperature cuprate superconductors consist of stacked CuO2 planes, with primarily two dimensional electronic band structures and magnetic excitations, while superconducting coherence is three dimensional. This dichotomy highlights the importance of out-of-plane charge dynamics, believed to be incoherent in the normal state, yet lacking a comprehensive characterization in energy-momentum space. Here, we use resonant inelastic x-ray scattering (RIXS) with polarization analysis to uncover the pure charge character of a recently discovered collective mode in electron-doped cuprates. This mode disperses along both the in- and, importantly, out-of-plane directions, revealing its three dimensional nature. The periodicity of the out-of-plane dispersion corresponds to the CuO2 plane distance rather than the crystallographic c-axis lattice constant, suggesting that the interplane Coulomb interaction drives the coherent out-of-plane charge dynamics. The observed properties are hallmarks of the long-sought acoustic plasmon, predicted for layered systems and argued to play a substantial role in mediating high temperature superconductivity., Comment: This is the version of first submission. The revised manuscript according to peer reviews is now accepted by Nature and will be published online on 31st Oct., 2018

The recently demonstrated x-ray scattering approach using a free electron laser with a high field pulsed magnet has opened new opportunities to explore the charge density wave (CDW) order in cuprate high temperature superconductors. Using this approach, we substantially degrade the superconductivity with magnetic fields up to 33 T to investigate the onset of CDW order in YBa$_2$Cu$_3$O$_x$ at low temperatures near a putative quantum critical point (QCP) at $p_1\sim $ 0.08 holes per Cu. We find no CDW can be detected in a sample with a doping concentration less than $p_1$. Our results indicate that the onset of the CDW ground state lies inside the zero-field superconducting dome, and broken translational symmetry is associated with the putative QCP at $p_1$, Comment: 4 figures

We investigated the doping dependence of magnetic excitations in the lightly doped cuprate La2-xSrxCuO4 via combined studies of resonant inelastic x-ray scattering (RIXS) at the Cu L3-edge and theoretical calculations. With increasing doping, the magnon dispersion is found to be essentially unchanged, but the spectral width broadens and the spectral weight varies differently at different momenta. Near the Brillouin zone center, we directly observe bimagnon excitations which possess the same energy scale and doping dependence as previously observed by Raman spectroscopy. They disperse weakly in energy-momentum space, and are consistent with a bimagnon dispersion that is renormalized by the magnon-magnon interaction at the zone center., Comment: 8 pages, 6 figures

The existence of charge density wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the ground state order has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to a dozen unit cells or less. Here we explore the CDW correlations in YBa2Cu3Ox (YBCO) ortho-II and ortho-VIII crystals, which belong to the cleanest available cuprate family, at magnetic fields in excess of the resistive upper critical field (Hc2) where the superconductivity is heavily suppressed. We find an incommensurate, unidirectional CDW with a well-defined onset at a critical field strength that is proportional to Hc2. It is related to but distinct from the short-range bidirectional CDW that exists at zero magnetic field. The unidirectional CDW possesses a long inplane correlation length as well as significant correlations between neighboring CuO2 planes, yielding a correlation volume that is at least 2 - 3 orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground-state of an "ideal" disorder-free cuprate.

The coupling between lattice and charge degrees of freedom in condensed matter materials is ubiquitous and can often result in interesting properties and ordered phases, including conventional superconductivity, charge density wave order, and metal-insulator transitions. Angle-resolved photoemission spectroscopy and both neutron and non-resonant x-ray scattering serve as effective probes for determining the behavior of appropriate, individual degrees of freedom -- the electronic structure and lattice excitation, or phonon dispersion, respectively. However, each provides less direct information about the mutual coupling between the degrees of freedom, usual through self-energy effects, which tend to renormalize and broaden spectral features precisely where the coupling is strong, impacting ones ability to quantitively characterize the coupling. Here we demonstrate that resonant inelastic x-ray scattering, or RIXS, can be an effective tool to directly determine the relative strength and momentum dependence of the electron-phonon coupling in condensed matter systems. Using a diagrammatic approach for an 8-band model of copper oxides, we study the contributions from the lowest order diagrams to the full RIXS intensity for a realistic scattering geometry, accounting for matrix element effects in the scattering cross-section as well as the momentum dependence of the electron-phonon coupling vertex. A detailed examination of these maps offers a unique perspective into the characteristics of electron-phonon coupling, which complements both neutron and non-resonant x-ray scattering, as well as Raman and infrared conductivity., Comment: 10 pages, 10 figures

Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_{2}$O$_{8+{\delta}}$ in the mid-infrared energy region. Combining photon-energy and momentum dependent RIXS measurements with theoretical calculations using exact diagonalization provides conclusive evidence that the Raman-like RIXS excitations correspond to collective spin excitations, which are magnons in the undoped Mott insulators and evolve into paramagnons in doped superconducting compounds. In contrast, the fluorescence-like shifts are due primarily to the continuum of particle-hole excitations in the charge channel. Our results show that under the proper experimental conditions RIXS indeed can be used to probe paramagnons in doped high-$T_c$ cuprate superconductors.

We performed ultrafast time-resolved near-infrared pump, resonant soft X-ray diffraction probe measurements to investigate the coupling between the photoexcited electronic system and the spin cycloid magnetic order in multiferroic TbMnO3 at low temperatures. We observe melting of the long range antiferromagnetic order at low excitation fluences with a decay time constant of 22.3 +- 1.1 ps, which is much slower than the ~1 ps melting times previously observed in other systems. To explain the data we propose a simple model of the melting process where the pump laser pulse directly excites the electronic system, which then leads to an increase in the effective temperature of the spin system via a slower relaxation mechanism. Despite this apparent increase in the effective spin temperature, we do not observe changes in the wavevector q of the antiferromagnetic spin order that would typically correlate with an increase in temperature under equilibrium conditions. We suggest that this behavior results from the extremely low magnon group velocity that hinders a change in the spin-spiral wavevector on these time scales., Comment: 9 pages, 4 figures

Charge density wave (CDW) correlations have recently been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured by x-ray scattering at zero and low fields. Here we combine a pulsed magnet with an x-ray free electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields up to 28 Tesla. While the zero-field CDW order, which develops below T ~ 150 K, is essentially two-dimensional, at lower temperature and beyond 15 Tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW onsets around the zero-field superconducting transition temperature, yet the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

Static strain in complex oxide heterostructures has been extensively used to engineer electronic and magnetic properties at equilibrium. In the same spirit, deformations of the crystal lattice with light may be used to achieve functional control across hetero-interfaces dynamically. Here, by exciting large amplitude infrared-active vibrations in a LaAlO3 substrate we induce magnetic order melting in a NdNiO3 film across a hetero-interface. Femtosecond Resonant Soft X-ray Diffraction is used to determine the spatial and temporal evolution of the magnetic disordering. We observe a magnetic melt front that grows from the substrate interface into the film, at a speed that suggests electronically driven propagation. Light control and ultrafast phase front propagation at hetero-interfaces may lead to new opportunities in optomagnetism, for example by driving domain wall motion to transport information across suitably designed devices., Comment: 35 pages, 8 Figures (both incl. Supplement)

Magnetic excitations in the optimally doped high-$T_\mathrm{c}$ superconductor Bi$_{1.5}$Pb$_{0.55}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+\delta}$ (OP-Bi2201, $T_\mathrm{c}\simeq 34$ K) are investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS), below and above the pseudogap opening temperature. At both temperatures the broad spectral distribution disperses along the (1,0) direction up to $\sim$350~meV at zone boundary, similarly to other hole-doped cuprates. However, above $\sim$0.22 reciprocal lattice units, we observe a concurrent intensity decrease for magnetic excitations and quasi-elastic signals with weak temperature dependence. This anomaly seems to indicate a coupling between magnetic, lattice and charge modes in this compound. We also compare the magnetic excitation spectra near the anti-nodal zone boundary in the single layer OP-Bi2201 and in the bi-layer optimally doped Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_2$O$_{8+\delta}$ (OP-Bi2212, $T_\mathrm{c}\simeq96$ K). The strong similarities in the paramagnon dispersion and in their energy at zone boundary indicate that the strength of the super-exchange interaction and the short-range magnetic correlation cannot be directly related to $T_\mathrm{c}$, not even within the same family of cuprates.

Ultrafast light pulses can modify the electronic properties of quantum materials by perturbing the underlying, intertwined degrees of freedom. In particular, iron-based superconductors exhibit a strong coupling among electronic nematic fluctuations, spins, and the lattice, serving as a playground for ultrafast manipulation. Here we use time-resolved x-ray scattering to measure the lattice dynamics of photo-excited BaFe2As2. Upon optical excitation, no signature of an ultrafast change of the crystal symmetry is observed, but the lattice oscillates rapidly in time due to the coherent excitation of an A1g mode that modulates the Fe-As-Fe bond angle. We directly quantify the coherent lattice dynamics and show that even a small photo-induced lattice distortion can induce notable changes in the electronic and magnetic properties. Our analysis implies that transient structural modification can generally be an effective tool for manipulating the electronic properties of multi-orbital systems, where electronic instabilities are sensitive to the orbital character of bands near the Fermi level.

We report femtosecond resonant soft X-ray diffraction measurements of the dynamics of the charge order and of the crystal lattice in non-superconducting, stripe-ordered La1.875Ba0.125CuO4. Excitation of the in-plane Cu-O stretching phonon with a mid-infrared pulse has been previously shown to induce a transient superconducting state in the closely related compound La1.675Eu0.2Sr0.125CuO4. In La1.875Ba0.125CuO4, we find that the charge stripe order melts promptly on a sub-picosecond time scale. Surprisingly, the low temperature tetragonal distortion is only weakly reduced, reacting on significantly longer time scales that do not correlate with light-induced superconductivity. This experiment suggests that charge modulations alone, and not the LTT distortion, prevent superconductivity in equilibrium., Comment: 16 pages, 3 figures

The momentum dependence of the superconducting gap in the cuprates has been debated, with most experiments reporting a deviation from a simple $d_{x^2-y^2}$ form in the underdoped regime and a few experiments claiming that a simple $d_{x^2-y^2}$ form persists down to the lowest dopings. We affirm that the superconducting gap function in sufficiently underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) deviates from a simple \textit{d}-wave form near the antinode. This is observed in samples where doping is controlled only by oxygen annealing, in contrast to claims that this effect is only seen in cation-substituted samples. Moreover, a quasiparticle peak is present at the antinode down to p$=$0.08, refuting claims that a deviation from a simple \textit{d}-wave form is a data analysis artifact stemming from difficulty in assessing a gap in the absence of a quasiparticle.

Bulk charge density modulations, recently observed in high critical-temperature ($T_\mathrm{c}$) cuprate superconductors, coexist with the so-called pseudogap and compete with superconductivity. However, its direct observation has been limited to a narrow doping region in the underdoped regime. Using energy-resolved resonant x-ray scattering we have found evidence for such bulk charge modulations, or soft collective charge modes (soft CCMs), in optimally doped Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_{2}$O$_{8+\delta}$ (Pb-Bi2212) around the summit of the superconducting dome with momentum transfer $q_{\parallel}\sim0.28$ reciprocal lattice units (r.l.u.) along the Cu-O bond direction. The signal is stronger at $T\simeq T_\mathrm{c}$ than at lower temperatures, thereby confirming a competition between soft CCMs and superconductivity. These results demonstrate that soft CCMs are not constrained to the underdoped regime, suggesting that soft CCMs appear across a large part of the phase diagram of cuprates and are intimately entangled with high-$T_\mathrm{c}$ superconductivity., Comment: 6 pages, 3 figures, 1 table

HgBa$_{2}$CuO$_{4+\delta}$ (Hg1201) has been shown to be a model cuprate for scattering, optical, and transport experiments, but angle-resolved photoemission spectroscopy (ARPES) data are still lacking owing to the absence of a charge-neutral cleavage plane. We report on progress in achieving the experimental conditions for which quasiparticles can be observed in the near-nodal region of the Fermi surface. The d-wave superconducting gap is measured and found to have a maximum of 39 meV. At low temperature, a kink is detected in the nodal dispersion at approximately 51 meV below the Fermi level, an energy that is different from other cuprates with comparable T$_c$. The superconducting gap, Fermi surface, and nodal band renormalization measured here provide a crucial momentum-space complement to other experimental probes.

We identify dd-excitations in the quasi-one dimensional compound Ca$_2$Y$_2$Cu$_5$O$_{10}$ using resonant inelastic x-ray scattering. By tuning across the Cu L$_3$-edge, we observe abrupt shifts in the dd-peak positions as a function of incident photon energy. This observation demonstrates orbital-specific coupling of the high-energy excited states of the system to the low-energy degrees of freedom. A Franck-Condon treatment of electron-lattice coupling, consistent with other measurements in this compound, reproduces these shifts, explains the Gaussian lineshapes, and highlights charge-orbital-lattice renormalization in the high energy d-manifold., Comment: 5 pages, 4 figures

High-temperature superconductivity (HTSC) mysteriously emerges upon doping holes or electrons into insulating copper oxides with antiferromagnetic (AFM) order. It has been thought that the large energy scale of magnetic excitations, compared to phonon energies for example, lies at the heart of an electronically-driven superconducting phase at high temperatures. However, despite extensive studies, little information is available for comparison of high-energy magnetic excitations of hole- and electron-doped superconductors to assess a possible correlation with the respective superconducting transition temperatures. Here, we use resonant inelastic x-ray scattering (RIXS) at the Cu L3-edge to reveal high-energy collective excitations in the archetype electron-doped cuprate Nd2-xCexCuO4 (NCCO). Surprisingly, despite the fact that the spin stiffness is zero and the AFM correlations are short-ranged, magnetic excitations harden significantly across the AFM-HTSC phase boundary, in stark contrast with the hole-doped cuprates. Furthermore, we find an unexpected and highly dispersive mode in superconducting NCCO that is undetected in the hole-doped compounds, which emanates from the zone center with a characteristic energy comparable to the pseudogap, and may signal a quantum phase distinct from superconductivity. The uncovered asymmetry in the high-energy collective excitations with respect to hole and electron doping provides additional constraints for modeling the HTSC cuprates., Comment: 23 pages, 8 figures, Submitted to Nature Physics

Using time-dependent Ginzburg-Landau theory, we study the role of amplitude and phase fluctuations in the recovery of charge and spin stripe phases in response to a pump pulse that melts the orders. For parameters relevant to the case where charge order precedes spin order thermodynamically, amplitude recovery governs the initial time scales, while phase recovery controls behavior at longer times. In addition to these intrinsic effects, there is a longer spin re-orientation time scale related to the scattering geometry that dominates the recovery of the spin phase. Coupling between the charge and spin orders locks the amplitude and similarly the phase recovery, reducing the number of distinct time scales. Our results well reproduce the major experimental features of pump-probe x-ray diffraction measurements on the striped nickelate La$_{1.75}$Sr$_{0.25}$NiO$_4$. They highlight the main idea of this work, which is the use of time-dependent Ginzburg-Landau theory to study systems with multiple coexisting order parameters.

We investigate the order parameter dynamics of the stripe-ordered nickelate, La$_{1.75}$Sr$_{0.25}$NiO$_4$, using time-resolved resonant X-ray diffraction. In spite of distinct spin and charge energy scales, the two order parameters' amplitude dynamics are found to be linked together due to strong coupling. Additionally, the vector nature of the spin sector introduces a longer re-orientation time scale which is absent in the charge sector. These findings demonstrate that the correlation linking the symmetry-broken states does not unbind during the non-equilibrium process, and the time scales are not necessarily associated with the characteristic energy scales of individual degrees of freedom., Comment: 4 figures. Accepted by Physical Review Letter

High resolution resonant inelastic x-ray scattering has been performed to reveal the role of lattice-coupling in a family of quasi-1D insulating cuprates, Ca$_{2+5x}$Y$_{2-5x}$Cu$_5$O$_{10}$. Site-dependent low energy excitations arising from progressive emissions of a 70 meV lattice vibrational mode are resolved for the first time, providing a direct measurement of electron-lattice coupling strength. We show that such electron-lattice coupling causes doping-dependent distortions of the Cu-O-Cu bond angle, which sets the intra-chain spin exchange interactions. Our results indicate that the lattice degrees of freedom are fully integrated into the electronic behavior in low dimensional systems., Comment: 5 pages, 4 figure

A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials such as the cuprate high temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping-and-temperature dependence ARPES study of spectral gaps in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212), covering much of the superconducting portion of the phase diagram. In the ground state, abrupt changes in near-nodal gap phenomenology give spectroscopic evidence for two potential quantum critical points, p$=$0.19 for the pseudogap phase and p$=$0.076 for another competing phase. Temperature dependence reveals that the pseudogap is not static below T$_c$ and exists p$>$0.19 at higher temperatures. Our data imply a revised phase diagram which reconciles conflicting reports about the endpoint of the pseudogap in the literature, incorporates phase competition between the superconducting gap and pseudogap, and highlights distinct physics at the edge of the superconducting dome., Comment: to appear in PNAS

The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerged in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of its ability to measure material properties at atomic and electronic time scales and create excited states not accessible by the conventional means can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here, combining time-resolved femotosecond optical and resonant x-ray diffraction measurements on striped La1.75Sr0.25NiO4, we reveal unforeseen photo-induced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, unlike thermal phase fluctuations near the critical temperature in equilibrium10. Importantly, relaxation of the phase fluctuations are found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limit charge order recovery. This discovery of new aspect to phase fluctuation provides more holistic view for the importance of phase in ordering phenomena of quantum matter., Comment: 23 pages, 6 figures. Published version can be found at Nature Communications 3, 838 (2012)

We performed resonant soft X-ray diffraction on known charge density wave (CDW) compounds, rare earth tri-tellurides. Near the $M_5$ (3d - 4f) absorption edge of rare earth ions, an intense diffraction peak is detected at a wavevector identical to that of CDW state hosted on Te$_2$ planes, indicating a CDW-induced modulation on the rare earth ions. Surprisingly, the temperature dependence of the diffraction peak intensity demonstrates an exponential increase at low temperatures, vastly different than that of the CDW order parameter. Assuming 4f multiplet splitting due to the CDW states,we present a model to calculate X-ray absorption spectrum and resonant profile of the diffraction peak, agreeing well with experimental observations. Our results demonstrate a situation where the temperature dependence of resonant X-ray diffraction peak intensity is not directly related to the intrinsic behavior of the order parameter associated with the electronic order, but is dominated by the thermal occupancy of the valence states., Comment: 7 pages, 5 figures

We report on the ultrafast dynamics of magnetic order in a single crystal of CuO at a temperature of 207 K in response to strong optical excitation using femtosecond resonant x-ray diffraction. In the experiment, a femtosecond laser pulse induces a sudden, nonequilibrium increase in magnetic disorder. After a short delay ranging from 400 fs to 2 ps, we observe changes in the relative intensity of the magnetic ordering diffraction peaks that indicate a shift from a collinear commensurate phase to a spiral incommensurate phase. These results indicate that the ultimate speed for this antiferromagnetic re-orientation transition in CuO is limited by the long-wavelength magnetic excitation connecting the two phases., Comment: Accepted by Physical Review Letters (Dec. 2, 2011)

Optical control of magnetism, of interest for high-speed data processing and storage, has only been demonstrated with near-infrared excitation to date. However, in absorbing materials, such high photon energies can lead to significant dissipation, making switch back times long and miniaturization challenging. In manganites, magnetism is directly coupled to the lattice, as evidenced by the response to external and chemical pressure, or to ferroelectric polarization. Here, femtosecond mid-infrared pulses are used to excite the lattice in La0.5Sr1.5MnO4 and the dynamics of electronic order are measured by femtosecond resonant soft x-ray scattering with an x-ray free electron laser. We observe that magnetic and orbital orders are reduced by excitation of the lattice. This process, which occurs within few picoseconds, is interpreted as relaxation of the complex charge-orbital-spin structure following a displacive exchange quench - a prompt shift in the equilibrium value of the magnetic and orbital order parameters after the lattice has been distorted. A microscopic picture of the underlying unidirectional lattice displacement is proposed, based on nonlinear rectification of the directly-excited vibrational field, as analyzed in the specific lattice symmetry of La0.5Sr1.5MnO4. Control of magnetism through ultrafast lattice excitation has important analogies to the multiferroic effect and may serve as a new paradigm for high-speed optomagnetism., Comment: 10 pages manuscript, 4 figures

Recent laser angle-resolved photoemission spectroscopy studies have established the presence of a new kink in the low-energy nodal dispersion of Bi$_2$Sr$_2$CaCu$_2$O$+{8+\delta}$ (Bi-2212). The energy scale (~8-15 meV) of this kink appears below the maximum of the superconducting gap $\delta_0$. Therefore it is difficult to interpret this feature in terms of the usual coupling to a sharp dispersionless mode. In this paper we examine electron-phonon coupling to the in-plane acoustic phonon branch arising from the modulation of the screened Coulomb potential. We demonstrate that such a coupling has a strong forward scattering peak, and as a consequence, a kink occurs in the dispersion at an energy scale shifted by the local gap $\delta(k)$. In addition, considerations for the reduction of screening with underdoping naturally explains the observed doping dependence of the low-energy kink. These results point to a strong coupling to the acoustic branch which is peaked in the forward scattering direction and has important implications for transport and pairing in the high-T$_c$ cuprates., Comment: 4.5 pages, 4 figures, Submitted to PRL

Nematicity, defined as broken rotational symmetry, has recently been observed in competing phases proximate to the superconducting phase in the cuprate high temperature superconductors. Similarly, the new iron-based high temperature superconductors exhibit a tetragonal to orthorhombic structural transition (i.e. a broken C4 symmetry) that either precedes or is coincident with a collinear spin density wave (SDW) transition in undoped parent compounds, and superconductivity arises when both transitions are suppressed via doping. Evidence for strong in-plane anisotropy in the SDW state in this family of compounds has been reported by neutron scattering, scanning tunneling microscopy, and transport measurements. Here we present an angle resolved photoemission spectroscopy study of detwinned single crystals of a representative family of electron-doped iron-arsenide superconductors, Ba(Fe1-xCox)2As2 in the underdoped region. The crystals were detwinned via application of in-plane uniaxial stress, enabling measurements of single domain electronic structure in the orthorhombic state. At low temperatures, our results clearly demonstrate an in-plane electronic anisotropy characterized by a large energy splitting of two orthogonal bands with dominant dxz and dyz character, which is consistent with anisotropy observed by other probes. For compositions x>0, for which the structural transition (TS) precedes the magnetic transition (TSDW), an anisotropic splitting is observed to develop above TSDW, indicating that it is specifically associated with TS. For unstressed crystals, the band splitting is observed close to TS, whereas for stressed crystals the splitting is observed to considerably higher temperatures, revealing the presence of a surprisingly large in-plane nematic susceptibility in the electronic structure., Comment: final version published in PNAS, including supplementary information

We present angle-resolved photoemission spectroscopy (ARPES) studies of the cuprate high-temperature superconductors which elucidate the relation between superconductivity and the pseudogap and highlight low-energy quasiparticle dynamics in the superconducting state. Our experiments suggest that the pseudogap and superconducting gap represent distinct states, which coexist below T$_c$. Studies on Bi-2212 demonstrate that the near-nodal and near-antinodal regions behave differently as a function of temperature and doping, implying that different orders dominate in different momentum-space regions. However, the ubiquity of sharp quasiparticles all around the Fermi surface in Bi-2212 indicates that superconductivity extends into the momentum-space region dominated by the pseudogap, revealing subtlety in this dichotomy. In Bi-2201, the temperature dependence of antinodal spectra reveals particle-hole asymmetry and anomalous spectral broadening, which may constrain the explanation for the pseudogap. Recognizing that electron-boson coupling is an important aspect of cuprate physics, we close with a discussion of the multiple 'kinks' in the nodal dispersion. Understanding these may be important to establishing which excitations are important to superconductivity., Comment: To appear in a focus issue on 'Fermiology of Cuprates' in New Journal of Physics

La-doped and Y-doped Bi2Sr2CaCu2O8+d (Bi2212) compounds Bi2Sr2-xLax(Ca,Y)Cu2O8+d, which range from the insulator to the deeply underdoped superconductor, have been studied by angle-resolved photoemission spectroscopy. We have observed that the lower Hubbard band (LHB) of the parent insulator is gradually shifted upward with doping without significantly changing the band dispersions, which implies a downward shift of the chemical potential with hole doping. This behaviour is analogous to Bi2Sr2-xLaxCuO6+d (Bi2201) and Ca2-xNaxCuO2Cl2 (Na-CCOC) but is different from La2-xSrxCuO4 (LSCO), where the LHB stays well below the chemical potential and does not move while its intensity quickly diminishes in the underdoped region., Comment: Submitted to PRB

The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi2Sr2CaCu2O8+d (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is non-universal, in contrast to assumed phenomenology. This is used together with laser-ARPES measurements of the gap velocity, v2, to resolve discrepancies with thermal conductivity measurements., Comment: Submitted to Phys. Rev. Lett

We first summarize the basic structure of the outer distribution module of a completely regular code. Then, employing a simple lemma concerning eigenvectors in association schemes, we propose to study the tightest case, where the indices of the eigenspace that appear in the outer distribution module are equally spaced. In addition to the arithmetic codes of the companion paper, this highly structured class includes other beautiful examples and we propose the classification of $Q$-polynomial completely regular codes in the Hamming graphs. A key result is Theorem 3.10 which finds that the $Q$-polynomial condition is equivalent to the presence of a certain Leonard pair. This connection has impact in two directions. First, the Leonard pairs are classified and we gain quite a bit of information about the algebraic structure of any code in our class. But also this gives a new setting for the study of Leonard pairs, one closely related to the classical one where a Leonard pair arises from each thin/dual-thin irreducible module of a Terwilliger algebra of some $P$- and $Q$-polynomial association scheme, yet not previously studied. It is particularly interesting that the Leonard pair associated to some code $C$ may belong to one family in the Askey scheme while the distance-regular graph in which the code is found may belong to another., Comment: 23 pages

In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression. In order to better understand these "arithmetic completely regular codes", we focus on cartesian products of completely regular codes and products of their corresponding coset graphs in the additive case. Employing earlier results, we are then able to prove a theorem which nearly classifies these codes in the case where the graph admits a completely regular partition into such codes (e.g, the cosets of some additive completely regular code). Connections to the theory of distance-regular graphs are explored and several open questions are posed., Comment: 26 pages, 1 figure

In this paper we present a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. We specifically discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice, and review how the wide range of materials dependence, such as the number of CuO$_2$ layers, and the doping dependence can be straightforwardly understood as arising due to novel electron-phonon coupling., Comment: 9 pages and 6 figures. Submitted as a review article for Advances in Condensed Matter Physics

Angle Resolved Photoemission Spectroscopy (ARPES) probes the momentum-space electronic structure of materials, and provides invaluable information about the high-temperature superconducting cuprates. Likewise, the cuprate real-space, inhomogeneous electronic structure is elucidated by Scanning Tunneling Spectroscopy (STS). Recently, STS has exploited quasiparticle interference (QPI) - wave-like electrons scattering off impurities to produce periodic interference patterns - to infer properties of the QP in momentum-space. Surprisingly, some interference peaks in Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} (Bi-2212) are absent beyond the antiferromagnetic (AF) zone boundary, implying the dominance of particular scattering process. Here, we show that ARPES sees no evidence of quasiparticle (QP) extinction: QP-like peaks are measured everywhere on the Fermi surface, evolving smoothly across the AF zone boundary. This apparent contradiction stems from different natures of single-particle (ARPES) and two-particle (STS) processes underlying these probes. Using a simple model, we demonstrate extinction of QPI without implying the loss of QP beyond the AF zone boundary.

Here we report the first angle-resolved photoemission measurement on nearly optimally-doped multi-layer Tl-based superconducting cuprates (Tl-2212 and Tl-1223) and a comparison study to single layer (Tl-2201) compound. A "kink" in the band dispersion is found in all three compounds but exhibits different momentum dependence for the single layer and multi-layer compounds, reminiscent to that of Bi-based cuprates. This layer number dependent renormalization effect strongly implies that the spin resonance mode is unlikely responsible for the dramatic renormalization effect near the antinodal region., Comment: 4 page, 5 figures