Enhanced Electron-Phonon Coupling for Charge-Density-Wave Formation in La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}.

Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu L_{3} edge resonant inelastic x-ray scattering, we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}. We investigate the interplay between charge order and EPC as a function of doping and temperature and find that the EPC is enhanced in a narrow momentum region around the CDW ordering vector. By detuning the incident photon energy from the absorption resonance, we extract an EPC matrix element at the CDW ordering vector of M≃0.36 eV, which decreases to M≃0.30 eV at high temperature in the absence of the CDW. Our results suggest a feedback mechanism in which the CDW enhances the EPC which, in turn, further stabilizes the CDW.

Anomalous density fluctuations in a strange metal.

A central mystery in high-temperature superconductivity is the origin of the so-called strange metal (i.e., the anomalous conductor from which superconductivity emerges at low temperature). Measuring the dynamic charge response of the copper oxides, [Formula: see text], would directly reveal the collective properties of the strange metal, but it has never been possible to measure this quantity with millielectronvolt resolution. Here, we present a measurement of [Formula: see text] for a cuprate, optimally doped Bi2.1Sr1.9CaCu2O8+x (Tc = 91 K), using momentum-resolved inelastic electron scattering. In the medium energy range 0.1-2 eV relevant to the strange metal, the spectra are dominated by a featureless, temperature- and momentum-independent continuum persisting to the electronvolt energy scale. This continuum displays a simple power-law form, exhibiting q2 behavior at low energy and q2/ω2 behavior at high energy. Measurements of an overdoped crystal (Tc = 50 K) showed the emergence of a gap-like feature at low temperature, indicating deviation from power law form outside the strange-metal regime. Our study suggests the strange metal exhibits a new type of charge dynamics in which excitations are local to such a degree that space and time axes are decoupled.

A practical superconducting-microcalorimeter X-ray spectrometer for beamline and laboratory science.

We describe a series of microcalorimeter X-ray spectrometers designed for a broad suite of measurement applications. The chief advantage of this type of spectrometer is that it can be orders of magnitude more efficient at collecting X-rays than more traditional high-resolution spectrometers that rely on wavelength-dispersive techniques. This advantage is most useful in applications that are traditionally photon-starved and/or involve radiation-sensitive samples. Each energy-dispersive spectrometer is built around an array of several hundred transition-edge sensors (TESs). TESs are superconducting thin films that are biased into their superconducting-to-normal-metal transitions. The spectrometers share a common readout architecture and many design elements, such as a compact, 65 mK detector package, 8-column time-division-multiplexed superconducting quantum-interference device readout, and a liquid-cryogen-free cryogenic system that is a two-stage adiabatic-demagnetization refrigerator backed by a pulse-tube cryocooler. We have adapted this flexible architecture to mate to a variety of sample chambers and measurement systems that encompass a range of observing geometries. There are two different types of TES pixels employed. The first, designed for X-ray energies below 10 keV, has a best demonstrated energy resolution of 2.1 eV (full-width-at-half-maximum or FWHM) at 5.9 keV. The second, designed for X-ray energies below 2 keV, has a best demonstrated resolution of 1.0 eV (FWHM) at 500 eV. Our team has now deployed seven of these X-ray spectrometers to a variety of light sources, accelerator facilities, and laboratory-scale experiments; these seven spectrometers have already performed measurements related to their applications. Another five of these spectrometers will come online in the near future. We have applied our TES spectrometers to the following measurement applications: synchrotron-based absorption and emission spectroscopy and energy-resolved scattering; accelerator-based spectroscopy of hadronic atoms and particle-induced-emission spectroscopy; laboratory-based time-resolved absorption and emission spectroscopy with a tabletop, broadband source; and laboratory-based metrology of X-ray-emission lines. Here, we discuss the design, construction, and operation of our TES spectrometers and show first-light measurements from the various systems. Finally, because X-ray-TES technology continues to mature, we discuss improvements to array size, energy resolution, and counting speed that we anticipate in our next generation of TES-X-ray spectrometers and beyond.

Observation of a Charge Density Wave Incommensuration Near the Superconducting Dome in Cu_{x}TiSe_{2}.

X-ray diffraction was employed to study the evolution of the charge density wave (CDW) in Cu_{x}TiSe_{2} as a function of copper intercalation in order to clarify the relationship between the CDW and superconductivity. The results show a CDW incommensuration arising at an intercalation value coincident with the onset of superconductivity at around x=0.055(5). Additionally, it was found that the charge density wave persists to higher intercalant concentrations than previously assumed, demonstrating that the CDW does not terminate inside the superconducting dome. A charge density wave peak was observed in samples up to x=0.091(6), the highest copper concentration examined in this study. The phase diagram established in this work suggests that charge density wave incommensuration may play a role in the formation of the superconducting state.

Surface Collective Modes in the Topological Insulators Bi_{2}Se_{3} and Bi_{0.5}Sb_{1.5}Te_{3-x}Se_{x}.

We used low-energy, momentum-resolved inelastic electron scattering to study surface collective modes of the three-dimensional topological insulators Bi_{2}Se_{3} and Bi_{0.5}Sb_{1.5}Te_{3-x}Se_{x}. Our goal was to identify the "spin plasmon" predicted by Raghu and co-workers [Phys. Rev. Lett. 104, 116401 (2010)]. Instead, we found that the primary collective mode is a surface plasmon arising from the bulk, free carriers in these materials. This excitation dominates the spectral weight in the bosonic function of the surface χ^{"}(q,ω) at THz energy scales, and is the most likely origin of a quasiparticle dispersion kink observed in previous photoemission experiments. Our study suggests that the spin plasmon may mix with this other surface mode, calling for a more nuanced understanding of optical experiments in which the spin plasmon is reported to play a role.

Electronic screening-enhanced hole pairing in two-leg spin ladders studied by high-resolution resonant inelastic x-ray scattering at Cu M edges.

We study the electronic screening mechanisms of the effective Coulomb on-site repulsion in hole-doped Sr(14)Cu(24)O(41) compared to undoped La(6)Ca(8)Cu(24)O(41) using polarization dependent high-resolution resonant inelastic x-ray scattering at Cu M edges. By measuring the energy of the effective Coulomb on-site repulsion and the spin excitations, we estimate superexchange and hopping matrix element energies along rungs and legs, respectively. Interestingly, hole doping locally screens the Coulomb on-site repulsion reducing it by as much as 25%. We suggest that the increased ratio of the electronic kinetic to the electronic correlation energy contributes to the local superexchange mediated pairing between holes.

Sequence of hole resonances in complex oxide heterostructures.

Resonant soft x-ray scattering measurements at the O K edge on Sr2CuO4-ν/La2NiO4+δ (SCO/LNO) complex oxide superlattices show resonances for holes in the two constituent layers, in a sequence of energy levels. The observation of well defined resonances, on a superlattice with layers one unit cell thick, indicates that the resonance energy is largely unaffected by atoms outside a cluster extending half a unit cell along the c axis, consistent with calculations for bulk materials. Comparison to measurements on related superlattices confirms that the order of resonances at the O K edge reflects the order of hole ground-state energies in the heterostructure buried layers. For the SCO/LNO superlattices, the measurements show that the ground-state energies remain different in very thin SCO and LNO layers, which is a contributing factor when considering electronic reconstruction at interfaces, in addition to the areal density of ionic charges in the atomic planes. Different hole energy levels in the SCO/LNO superlattice also imply that holes do not spread into SCO from LNO layers.

Form factor dispersion at La M5,4 edges and average density of resonant atoms.

Resonant soft x-ray scattering on complex oxide superlattices shows very large variations in the superlattice reflection position and intensity near La M5,4 edges. Resonant dispersion of the La x-ray form factor describes the observations well. We determine the average density of resonant La atoms and the thickness of superlattice layers.

Inelastic light scattering measurements of a pressure-induced quantum liquid in KCuF3.

Pressure-dependent, low-temperature inelastic light (Raman) scattering measurements of KCuF(3) show that applied pressure above P* ~ 7 kbar suppresses a previously observed structural phase transition temperature to zero temperature in KCuF(3), resulting in the development of a fluctuational (quasielastic) response near T ~ 0 K. This pressure-induced fluctuational response--which we associate with slow fluctuations of the CuF(6) octahedral orientation--is temperature independent and exhibits a characteristic fluctuation rate that is much larger than the temperature, consistent with quantum fluctuations of the CuF(6) octahedra. A model of pseudospin-phonon coupling provides a qualitative description of both the temperature- and pressure-dependent evolution of the Raman spectra of KCuF(3).

Fragile magnetic ground state in half-doped LaSr2Mn2O7.

We investigated the orbital and antiferromagnetic ordering behaviors of the half-doped bilayer manganite La(2-2x)Sr(1+2x)Mn2O7 (x ≃ 0.5) by using Mn L(2,3)-edge resonant soft x-ray scattering. Resonant soft x-ray scattering reveals the CE-type orbital order below T(oo) ≃ 220 K, which shows partial melting behavior below T(m) ≃ 165 K. We also found coexistence CE- and A-type antiferromagnetic orders. Both orders involve the CE-type orbital order with nearly the same orbital character and are coupled with each other. These results manifest that the ground state with the CE-type antiferromagnetic order is easily susceptible to destabilization into the A-type one even with a small fluctuation of the doping level, as suggested by the extremely narrow magnetic phase boundaries at x ≃ 0.5±0.005.

Experimental observation of the crystallization of a paired holon state.

An excitation at 201 meV is observed in the doped-hole ladder cuprate Sr14Cu24O41, using ultraviolet resonance Raman scattering with incident light at 3.7 eV polarized along the rungs. The excitation is of charge nature, with a temperature independent excitation energy, and can be understood via an intraladder pair-breaking process. The intensity tracks closely the order parameter of the charge density wave in the ladder CDW(L), but persists above its transition temperature T(CDW(L)), indicating a strong local pairing above the T(CDW(L)). The 201 meV excitation vanishes in La6Ca8Cu24O(41+δ), and La5Ca9Cu24O41 which are samples with no holes in the ladders. Our results suggest that the doped holes in the ladder are composite bosons consisting of paired holons that order below T(CDW).

Mapping the magnetostructural quantum phases of Mn3O4.

We present temperature-dependent x-ray diffraction and temperature- and field-dependent Raman scattering studies of single-crystal Mn3O4, which reveal the magnetostructural phases that evolve in the spinels due to the interplay between strong spin-orbital coupling, geometric frustration, and applied magnetic field. We present evidence that the magnetoelastic and magnetodielectric behavior in this material is governed by magnetic-field-controlled tetragonal-to-monoclinic phase changes. Most interestingly, for an applied field transverse to the ferrimagnetic ordering direction, H parallel [110], we find evidence for a field-tuned quantum phase transition to a tetragonal spin-disordered phase, indicating that a structurally symmetric, spin frustrated phase can be recovered at T approximately 0 for intermediate transverse fields in Mn3O4.

Superconducting transition at 38 K in insulating-overdoped La2CuO4-La1.64Sr0.36CuO4 superlattices: evidence for interface electronic redistribution from resonant soft X-ray scattering.

We use resonant soft x-ray scattering (RSXS) to quantify the hole distribution in a superlattice of insulating La2CuO4 (LCO) and overdoped La2-xSrxCuO4 (LSCO). Despite its nonsuperconducting constituents, this structure is superconducting with T_{c}=38 K. We found that the conducting holes redistribute electronically from LSCO to the LCO layers. The LCO layers were found to be optimally doped, suggesting they are the main drivers of superconductivity. Our results demonstrate the utility of RSXS for separating electronic from structural effects at oxide interfaces.

Quantum and classical mode softening near the charge-density-wave-superconductor transition of CuxTiSe2.

Temperature- and x-dependent Raman scattering studies of the charge-density-wave (CDW) amplitude modes in Cu(x)TiSe(2) show that the amplitude mode frequency omega(0) exhibits identical power-law scaling with the reduced temperature T/T(CDW) and the reduced Cu content x/x(c), i.e., omega(0) approximately (1-p)(0.15) for p=T/T(CDW) or x/x(c), suggesting that mode softening is independent of the control parameter used to approach the CDW transition. We provide evidence that x-dependent mode softening in Cu(x)TiSe(2) is associated with the reduction of the electron-phonon coupling constant, and that x-dependent "quantum" (T approximately 0) mode softening suggests the presence of a quantum critical point within the superconductor phase of Cu(x)TiSe(2).

Strain amplification of the 4k_(F) chain instability in Sr14Cu24O41.

We used resonant soft x-ray scattering to study the chain ordering in Sr14Cu24O41 (SCO). We observed, for the first time, both the chain and ladder orders in SCO with the same probe. We found that the chain modulation in SCO is incommensurate with wave vector L_(c)=0.318, is strongly temperature (T) dependent, and is accompanied by a substantial hole modulation. By contrast, the chain modulation in a hole-depleted control sample La6Ca8Cu24O41 was commensurate (L_(c)=0.3), T independent, and purely structural. We conclude that the chain charge order in SCO is a 4k_(F) charge density wave stabilized by the misfit strain between the ladder and chain substructures.

Quantum melting of the hole crystal in the spin ladder of Sr(14-x)CaxCu24O41.

We have used resonant soft x-ray scattering to study the effects of discommensuration on the hole Wigner crystal (HC) in the spin ladder Sr(14-x)CaxCu24O41 (SCCO). As the hole density is varied the HC forms only with the commensurate wave vectors L(L) = 1/5 and L(L) = 1/3; for incommensurate values it "melts." A simple scaling between L(L) and temperature is observed, tau1/3/tau1/5 = 5/3, indicating an inverse relationship between the interaction strength and wavelength. Our results suggest that SCCO contains hole pairs that are crystallized through an interplay between lattice commensuration and Coulomb repulsion, reminiscent of the "pair density wave" scenario.

Crystallization of charge holes in the spin ladder of Sr14Cu24O41.

Determining the nature of the electronic phases that compete with superconductivity in high-transition-temperature (high-T(c)) superconductors is one of the deepest problems in condensed matter physics. One candidate is the 'stripe' phase, in which the charge carriers (holes) condense into rivers of charge that separate regions of antiferromagnetism. A related but lesser known system is the 'spin ladder', which consists of two coupled chains of magnetic ions forming an array of rungs. A doped ladder can be thought of as a high-T(c) material with lower dimensionality, and has been predicted to exhibit both superconductivity and an insulating 'hole crystal' phase in which the carriers are localized through many-body interactions. The competition between the two resembles that believed to operate between stripes and superconductivity in high-T(c) materials. Here we report the existence of a hole crystal in the doped spin ladder of Sr14Cu24O41 using a resonant X-ray scattering technique. This phase exists without a detectable distortion in the structural lattice, indicating that it arises from many-body electronic effects. Our measurements confirm theoretical predictions, and support the picture that proximity to charge ordered states is a general property of superconductivity in copper oxides.

Soft x-ray resonant diffraction study of magnetic and orbital correlations in a manganite near half doping.

We have utilized resonant x-ray diffraction at the Mn L(II,III) edges in order to directly compare magnetic and orbital correlations in Pr0.6Ca0.4MnO3. Comparing the widths of the magnetic and orbital diffraction peaks, we find that the magnetic correlation length exceeds that of the orbital order by nearly a factor of 2. Furthermore, we observe a large (approximately 3 eV) spectral weight shift between the magnetic and orbital resonant line shapes, which cannot be explained within the classic Goodenough picture of a charge-ordered ground state. To explain the shift, we calculate the orbital and magnetic resonant diffraction line shapes based on a relaxed charge-ordered model.

Imaging density disturbances in water with a 41.3-attosecond time resolution.

We show that the momentum flexibility of inelastic x-ray scattering may be exploited to invert its loss function, allowing real time imaging of density disturbances in a medium. We show the disturbance arising from a point source in liquid water, with a resolution of 41.3 attoseconds (4.13 x 10(-17) s) and 1.27 A (1.27 x 10(-8) cm). This result is used to determine the structure of the electron cloud around a photoexcited chromophore in solution, as well as the wake generated in water by a 9 MeV gold ion. We draw an analogy with pump-probe techniques and suggest that energy-loss scattering may be applied more generally to the study of attosecond phenomena.

A structural probe of the doped holes in cuprate superconductors.

An unresolved issue concerning cuprate superconductors is whether the distribution of carriers in the CuO2 plane is uniform or inhomogeneous. Because the carriers comprise a small fraction of the total charge density and may be rapidly fluctuating, modulations are difficult to detect directly. We demonstrate that in anomalous x-ray scattering at the oxygen K edge of the cuprates, the contribution of carriers to the scattering amplitude is selectively magnified 82 times. This enhances diffraction from the doped holes by more than 10(3), permitting direct structural analysis of the superconducting ground state. Scattering from thin films of La2CuO4+delta (superconducting transition temperature = 39 K) at temperature = 50 +/- 5 kelvin on the reciprocal space intervals (0,0,0.21) --> (0,0,1.21) and (0,0,0.6) --> (0.3,0,0.6) shows a rounding of the carrier density near the substrate suggestive of a depletion zone or similar effect. The structure factor for off-specular scattering was less than 3 x 10(-7) electrons, suggesting an absence of in-plane hole ordering in this material.