Dynamical Charge Correlation Research Articles

Low-energy quasi-circular electron correlations with charge order wavelength in Bi2Sr2CaCu2O8+δ.

Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over the qx-qy scattering plane in underdoped Bi2Sr2CaCu2O8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in the qx-qy scattering plane with radius equal to the magnitude of the charge order wave vector, qCO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [qx = ±qCO, qy = 0] and [qx = 0, qy = ±qCO]) as the origin of the observed correlations.

Phonon spectrum of underdoped HgBa2CuO4+δ investigated by neutron scattering

The cuprates exhibit a prominent charge-density-wave (CDW) instability with wavevector along [100], i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wavevector approximately half-way through the Brillouin zone. Most of this work has focused on moderately-doped cuprates, for which the CDW order is robust, or on optimally-doped samples, for which the superconducting transition temperature ($T_c$) attains its maximum. Here we present a time-of-flight neutron scattering study of phonons in simple-tetragonal $\text{HgBa}_2\text{CuO}_{4+\delta}$ ($T_c = 55$ K) at a low doping level where prior work showed the CDW order to be weak. We employ and showcase a new software-based technique that mines the large number of measured Brillouin zones for useful data in order to improve accuracy and counting statistics. Density-functional theory has not provided an accurate description of phonons in $\text{HgBa}_2\text{CuO}_{4+\delta}$, yet we find the right set of parameters to qualitatively reproduce the data. The notable exception is a dispersion minimum in the longitudinal Cu-O bond-stretching branch along [100]. This discrepancy suggests that, while CDW order is weak, there exist significant dynamic charge correlations in the optic phonon range at low doping, near the edge of the superconducting dome.

Charge Dynamics in a Correlated Fermion System on a Geometrically Frustrated Lattice

Charge dynamics in an interacting fermionic model on a geometrically frustrated lattice are examined. We analyze a spinless fermion model on a paired triangular lattice, an electronic model for layered iron oxides, at zero and finite temperatures by the exact diagonalization methods. We focus on the two charge-ordered (CO) phases, termed CO1/2 and CO1/3, which, respectively, are realized by the intersite Coulomb interaction and quantum/thermal fluctuations. The optical spectra in CO1/3 show multiple components and their low-energy weights survive even below the ordering temperature (TCO). The changes in the dynamical charge correlation below TCO in CO1/3 are weakly momentum-dependent, in sharp contrast to those in CO1/2. These characteristic dynamics in CO1/3 are attributable to charge frustration effects and reproduce some aspects of the recent experimental optical and X-ray scattering spectra.

Resonant inelastic x-ray scattering study of intraband charge excitations in hole-doped high-Tccuprates

We have performed resonant inelastic x-ray scattering (RIXS) near the Cu-K edge on cuprate superconductors La(2-x)Sr(x)CuO(4), La(2-x)Ba(x)CuO(4), La(2-x)Sr(x)Cu(1-y)Fe(y)O(4) and Bi(1.76)Pb(0.35)Sr(1.89)CuO(6+d), covering underdoped to heavily overdoped regime and focusing on charge excitations inside the charge-transfer gap. RIXS measurements of the 214 systems with Ei = 8.993 keV have revealed that the RIXS intensity at 1 eV energy transfer has a minimum at (0,0) and maxima at (0.4pi, 0) and $(0, 0.4pi) for all doping points regardless of the stripe ordered state, suggesting that the corresponding structure is not directly related to stripe order. Measurements with Ei = 9.003 keV on metallic La(1.7)Sr(0.3)CuO(4) and Bi(1.76)Pb(0.35)Sr(1.89)CuO(6+d) exhibit a dispersive intra-band excitation below 4 eV, similar to that observed in the electron-doped Nd(1.85)Ce(0.15)CuO(4). This is the first observation of a dispersive intra-band excitation in a hole doped system, evidencing that both electron and hole doped systems have a similar dynamical charge correlation function.

Inelastic X-ray Scattering Studies of Electronic Excitations

Inelastic x-ray scattering (IXS) has developed into one of the most powerful momentum-resolved spectroscopies. Especially in the last decade, it has achieved significant progress utilizing brilliant x-rays from third-generation synchrotron radiation facilities. Simultaneously, theoretical efforts have been made to predict or interpret the experimental spectra. One of the scientific fields studied intensively by IXS is strongly correlated electron systems, where the interplay of charge, spin, and orbital degrees of freedom determines their physical properties. IXS can provide a new insight into the electron dynamics of the systems through the observation of charge, spin, and orbital excitations. Focusing on the momentum-resolved electronic excitations in strongly correlated electron systems, we review IXS studies and the present capabilities of IXS for the study of the dynamics of materials. With nonresonant inelastic x-ray scattering (NIXS), one can directly obtain dynamical charge correlation and we disc...

Theoretical Study of Resonant Inelastic X-ray Scattering Spectrum in Nickelates

We examine theoretically the Resonant Inelastic X-ray Scattering (RIXS) spectra on nickelates by using numerically exact diagonalization techniques on the two-band Hubbard model. Other spectra such as the dynamical charge correlation function are examined to discuss what excitations appear in the RIXS. We demonstrate that the spectra which appear upon doping in the dynamical charge correlation function and the RIXS are originated from only high spin states, in contrast to the optical conductivity where the spectrum comes from both high and low spin states.

Charge dynamics of electronic ferroelectricity in geometrically frustrated lattice

Charge dynamics in electronic ferroelectric materials, where electronic charge order is responsible for the electric polarization, is studied. Motivated from the layered iron oxide LuFe2O4 with a frustrated geometrical lattice, we introduce the spin-less fermion V-t model in a paired triangular lattice. This model is analyzed by utilizing the exact diagonalization method with the Lanczos algorithm in finite-size clusters. In particular, we focus on frustration effects on the charge dynamics. In the calculation of the ground state phase diagram, the non-polar two-fold charge order (CO) and the polar three-fold CO appear. In the optical conductivity spectra in the polar three-fold CO phase, multiple-peak structures appear in a wide energy range, in contrast to the spectra in the non-polar two-fold CO phase. This is originated from the non-equivalent two sublattices in the three-fold CO phase. The dynamical charge correlation function in the non-polar two-fold CO phase shows low-energy excitation at the wave vectors which correspond to the three-fold CO. This feature becomes remarkable near the phase boundary between the two-fold and three-fold CO phases. These precursor effects are attributed to the frustrated charge ordered system.

Dynamic charge correlations near the Peierls transition

The quantum phase transition between a repulsive Luttinger liquid and an insulating Peierls state is studied in the framework of the one-dimensional spinless Holstein model. We focus on the adiabatic regime but include the full quantum dynamics of the phonons. Using continuous-time quantum Monte Carlo simulations, we track in particular the dynamic charge structure factor and the single-particle spectrum across the transition. With increasing electron-phonon coupling, the dynamic charge structure factor reveals the emergence of a charge gap, and a clear signature of phonon softening at the zone boundary. The single-particle spectral function evolves continuously across the transition. Hybridization of the charge and phonon modes of the Luttinger liquid description leads to two modes, one of which corresponds to the coherent polaron band. This band acquires a gap upon entering the Peierls phase, whereas the other mode constitutes the incoherent, high-energy spectrum with backfolded shadow bands. Coherent polaronic motion is a direct consequence of quantum lattice fluctuations. In the strong-coupling regime, the spectrum is described by the static, mean-field limit. Importantly, whereas finite electron density in general leads to screening of polaron effects, the latter reappear at half filling due to charge ordering and lattice dimerization.

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbour Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a plasmon-like mode which, for wavevectors close to (pi,pi), increases in amplitude and softens as the charge ordering transition is approached. We propose that inelastic X-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with dxy symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge ordering transition.

Theoretical study of orbital excitations by resonant inelastic X-ray scattering in doped manganites

Resonant inelastic X-ray scattering in doped ferromagnetic manganites with orbital disorder is examined by using the exact diagonalisation method in finite size cluster systems. The calculated spectra of the dynamical charge correlation functions consist of the intra-band and inter-band excitations. The intensity corresponding to the intra-band excitations increases with doping of holes. This feature is consistent with the recent experiments of the resonant inelastic X-ray scattering in La 1− x Sr x MnO 3 ( x=0.2, and 0.4).

Fluctuation effects of nonlinear coupling between spin and charge excitations on dynamical correlation functions of the one-dimensional extended Hubbard model

We study fluctuation effects of nonlinear coupling between spin and charge excitations on dynamical correlation functions of the one-dimensional extended Hubbard model at half-filling. Two kinds of dynamical correlation functions, dynamical spin- and charge-correlation functions, are calculated by means of a quantum Monte Carlo simulation. We show that the dynamical spin-correlation function has a new peak on the high-energy side of the well-known magnon peak. Since this peak always appears above the charge-excitation gap, it should originate from a charge fluctuation induced through a final-state interaction of magnon creation. We also show that in the dynamical charge-correlation function, a charge-transfer excitation peak is broadened by fluctuation effects due to magnons. These results clearly show that spin and charge excitations are nonlinearly coupled in this system.

Critical Properties in Dynamical Charge Correlation Function for the One-Dimensional Mott Insulator

Critical properties in the dynamical charge correlation function for the one-dimensional Mott insulator are studied. By properly taking into account {\it the final-state interaction} between the charge and spin degrees of freedom, we find that the edge singularity in the charge correlation function is governed by massless spinon excitations, although it is naively expected that spinons do not directly contribute to the charge excitation over the Hubbard gap. We obtain the momentum-dependent anomalous critical exponent by applying the finite-size scaling analysis to the Bethe ansatz solution of the half-filled Hubbard model.