Charge Excitation Spectrum Research Articles

Memory-function approach to the normal-state optical properties of the Bechgaard salt (TMTSF) 2PF 6

The gauge invariant, two-component optical conductivity model, with a correlation gap structure related to the umklapp scattering processes, is applied to the quasi-one-dimensional electronic systems, and compared to the recent measurements on the Bechgaard salt (TMTSF) 2PF 6. The optical response of both the insulating and metallic state is found for the half-filled conduction band, depending on the ratio between the correlation energy scale 2 Δ 2 0 and the transfer integral in the direction perpendicular to the conducting chains, t b′ . The estimated value 2 Δ 2 0/ t b′ agrees reasonably well with the previous experimental and theoretical conclusions. Parallel to the chains the thermally activated conduction electrons in the insulating state are found to exhibit an universal behaviour, accounting for the observed single-particle optical conductivity of the ordered ground state of charge–density–wave systems. The band parameters and the related damping energies suitable to the normal metallic state of (TMTSF) 2PF 6 are estimated from the measured spectra. Not only the spectral weights but also the damping energies clearly indicate an opening of the correlation gap in the charge excitation spectrum.

Spin gap formation in the heavy fermion skutterudite compoundCeRu4Sb12

${\mathrm{CeRu}}_{4}{\mathrm{Sb}}_{12}$ is a mixed-valence Kondo-lattice system with a gap of 47 meV opening in the charge excitation spectrum, measured by the infrared spectroscopy technique. In order to study the temperature and energy and momentum dependence of the spin excitation spectrum, we have made inelastic neutron scattering measurements over a wide range of temperature between 5 and 250 K with an incident neutron energy of 100 meV. Our results measured at 5 and 60 K show that a spin gap of $\ensuremath{\sim}30\mathrm{meV}$ opens in the magnetic spectrum and above it the inelastic magnetic response forms a continuum right up to 95 meV. Surprisingly, the spin gap shows neither wave vector Q dependence within our resolution nor temperature dependence from 5 to 100 K. On the other hand, the spin gap starts to fill up above 100 K and the magnetic response becomes purely quasielastic at higher temperatures. The dramatic change observed above 100 K can be related to the coherence temperature of the Ce $4f$ electrons while the observed Q independence of the spin gap implies that single-ion Kondo interactions are important in the gap formation mechanism. We discuss our results in terms of theoretical models.

Numerical study of phonon spectra in strongly correlated electron systems

We examine theoretically the phonon dynamics in the electron–phonon-coupled systems. The model Hamiltonian is a one-dimensional Hubbard model coupled with phonons. The numerically exact diagonalization of the Hamiltonian with truncations of phonon Hilbert space is performed. We calculate the phonon excitation spectra and find a diffusive feature in the spectra in the metallic region. We also calculate the charge and spin excitation spectra and find that the feature in the phonon spectra is caused by the low energy electronic excitations.

Effect of Electron Correlation on Phonon Spectra in Cuprates

We examine theoretically the phonon dynamics in the electron-phonon-coupled systems. The model Hamiltonian is a one-dimensional Hubbard model where the hopping of electrons induces the electron-phonon coupling. The numerically exact diagonalization of the Hamiltonian with truncation of the total number of phonons is performed. We calculate the phonon excitation spectra and find that the softening of phonons occurs in insulating case, and a diffusive character appears in the metallic case. We also calculate the charge and spin excitation spectra and find that the dynamics of the phonon coupled with the hopping of electrons is affected by the low energy charge and spin excitations.

Elementary excitation for the orbitally degenerate Anderson model at finite temperatures

The elementary excitation for the orbitally degenerate Anderson model at finite temperatures is studied using the Bethe ansatz solution. The formulation of the elementary excitation at finite temperatures is based on the method which was first developed by Yang and Yang for the one-dimensional boson system with the $\ensuremath{\delta}$-function type interaction. The expressions of the elementary excitation energy for the spin and the charge degrees of freedom are derived. Using the obtained expressions, the spin and the charge excitation spectrums are calculated numerically. With decreasing temperature, the peak structure grows in the spin excitation spectrum, whereas the weight around the impurity level increases in the charge excitation spectrum, below the temperature corresponding to the characteristic energy scale of the system. The crystalline-field effects on the elementary excitation spectrums are investigated in the Kondo regime, and the results are discussed in connection with the difference in the Kondo temperature. The relation between the obtained results and the thermodynamic quantity of the orbitally degenerate Anderson model is also discussed.

Currents and moduli in the (4,0) theory

We consider black strings in five dimensions and their description as a (4,0) CFT. The CFT moduli space is described explicitly, including its subtle global structure. BPS conditions and global symmetries determine the spectrum of charged excitations, leading to an entropy formula for near-extreme black holes in four dimensions with arbitrary charge vector. In the BPS limit, this formula reduces to the quartic E(7,7) invariant. The prospects for a description of the (4,0) theory as a solvable CFT are explored.

The optical properties of the correlated two-dimensional 2h-tase 2 system

We discuss the optical response of the two-dimensional (2D) dichalcogenide 2H-TaSe 2. Our findings suggest a dynamics of the charge excitation spectrum dominated by two relevant features: a Drude contribution, which narrows with decreasing temperature, and a broad pseudogap-like feature in the mid-infrared range, which is present at all temperatures below 300 K.

Optical properties of Sr 14− xCa xCu 24O 41 and Sr 0.73CuO 2

The optical reflectivity as a function of temperature of the title compounds has been measured over a broad spectral range from 4 meV up to 12 eV. On the one hand, our findings suggest a very anisotropic dynamics of the charge excitation spectrum when measuring along or perpendicular to the ladders in Sr 14− x Ca x Cu 24O 41. On the other hand, the investigation of Sr 0.73CuO 2 allows us to study the electrodynamics of hole doped CuO 2 chains alone without complications arising from the presence of Cu 2O 3 ladders in Sr 14− x Ca x Cu 24O 41.

Spin and charge fluctuations in the t– J model

Dynamical spin and charge susceptibilities are calculated for the t– J model in the paramagnetic phase. Spin dynamics is scaled with the exchange interaction J and has a diffusive character in the hydrodynamic limit while the high frequency region shows a spin-wave-like excitation character. The charge excitation spectrum has a damped sound-like propagation mode for small wave vectors and a broad high energy peak (∼ t) for large momenta.

Temperature dependence of the anisotropic electrodynamics in the ladder compounds

The optical reflectivity as a function of temperature of the title compound for x =0 ; 5a nd 12 has been measured over a broad spectral range from 4 meV up to 12 eV. Our ndings suggest a very anisotropic dynamics of the charge excitation spectrum when measuring along or perpendicular to the ladders. Moreover, a metal-insulator transition develops at low temperatures, leading to a suppression of Drude spectral weight in the far and mid-infrared spectral range. We identify this behaviour as a consequence of the localization eects for small Ca substitution, and of the possible formation of a charge density wave condensate for large Ca substitution.

Elementary excitations for the Anderson model at finite temperatures

The elementary excitation spectrums for the Anderson model at finite temperatures are calculated by using the Bethe-ansatz solution. The formulation is based on the method of Yang and Yang, which was developed for the one-dimensional boson systems with the -function type interaction. We obtain the temperature dependence of the spin and the charge excitation spectrums. When the impurity level lies deeply from the Fermi level and the Coulomb interaction is suitably large, the resonant peak structure develops in the low energy region of the spin excitation spectrum and the hump structure grows around the impurity level of the charge excitation spectrum with decreasing temperature.

Electron concentration and on-site interaction effects for the spin and charge excitation spectra in the two-dimensional Hubbard model

Electron concentration and on-site interaction effects for spin and charge excitations in the two-dimensional Hubbard model are investigated. Using the auxiliary boson approach, which takes into account the spin and charge fluctuation effects, we derive an effective model which reproduces qualitatively well electronic states for the weak- and intermediate-coupling Hubbard models. The spin response function shows drastic changes as a function of the interaction and of the electron concentration. For the intermediate coupling regime, the Stoner enhancement around $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ and the spin-density-wave-like collective mode are obtained. In contrast, the charge response function does not have any specific structure for this interaction range. Finally, the electron concentration dependence of the zero sound velocity is discussed for the weak-coupling regime. The zero sound mode is shown to have a specific doping dependence that is associated with the existence of a hopping in the lattice.

Dynamics of Correlated Two-Dimensional Materials: The2H−TaSe2Case

We report a study of dc transport properties up to 600 K and of the optical response over a broad spectral range of the two-dimensional (2D) dichalcogenide $2H\ensuremath{-}{\mathrm{TaSe}}_{2}$. Our findings suggest a dynamics of the charge excitation spectrum dominated by two relevant features: a Drude contribution, which narrows with decreasing temperature, and a broad pseudogaplike feature in the midinfrared range, which is present at all temperatures below 300 K. The implications of these results with respect to the charge-density-wave phase transition at 122 K and more generally for the excitation spectrum of 2D correlated systems, e.g., the high temperature superconducting cuprates, will be addressed.

Nonexistence ofdx2−y2superconductivity in the Hubbard model

It is rigorously shown that the two-dimensional Hubbard model with narrow bands (including next-nearest-neighbor hopping, etc.) does not exhibit ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing long-range order at any nonzero temperature. This kind of pairing long-range order will also be excluded at zero temperature if an excited energy gap opens in the charge excitation spectrum of the system. These results hold true for both repulsive and attractive Coulomb interactions and for any electron fillings, and are consistent with quantum Monto Carlo calculations.

A−bplane optical conductivity inYBa2Cu3O7−δabove and belowT*

Analysis of the a-b plane optical conductivity $\sigma_{ab}$ for both twinned and untwinned YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ as a function of temperature and doping shows that below a well defined temperature T*, a dip in the spectrum systematically appears separating the infrared charge excitation spectrum into two components with distinct energy scales. The change from monotonic behaviour in $\sigma_{ab}$ is found to be concurrent with the onset of phonon anomalies in Raman and infrared spectra below T*. The optical data are suggested to be evidence for the appearance of an inhomogeneous distribution of carriers rather than the opening of a simple gap for charge excitations below T*, an interpretation wich is consistent with recent angle-resoved photoemission and electronic Raman spectra. We find that the behaviour below T* and the absence of any anomalies at Tc can be interpreted assuming a Bose-Einstein condensation of preformed pairs.

Phase transition in the one-dimensional Kondo lattice model with attractive electron-electron interaction

The one-dimensional Kondo lattice model with attractive interaction among the conduction electrons is analyzed in the case of half-filling. It is shown that there are three distinct phases depending on the coupling constants of the model. Two phases have a spin and charge gap. While one shows a clear distinction of the spin and charge excitation spectrum the other phase may be characterized as a band insulator type where both excitations are due to two-particle states. The third phase is gapless in both channels and has quasi-long-range order in the spin- and charge-density-wave correlation. In this phase the spin and charge excitations have a clearly separated spectrum. For the analysis we discuss first two limiting cases. Then a density matrix renormalization group calculation on finite systems is applied to determine the phase diagram and the correlation functions in the gapped and gapless phase for general coupling constants.

Critical Properties of Spectral Functions for the 1D Anisotropict-JModels with an Energy Gap

We exactly calculate the momentum-dependent critical exponents for spectral functions in the one-dimensional anisotropic t-J models with a gap either in the spin or charge excitation spectrum. Our approach is based on the Bethe ansatz technique combined with finite-size scaling techniques in conformal field theory. It is found that the spectral functions show a power-law singularity, which occurs at frequencies determined by the dispersion of a massive spin (or charge) excitation.We discuss how the nontrivial contribution of a massive excitation controls the singular behavior in optical response functions.

Electronic excitations in strongly correlated systems; 1D vs. 2D

The single-particle, spin and charge excitation spectra in one- (1D), two-dimensional (2D) and two-leg-ladder t- J models are presented in the exact diagonalization technique. In 1D, the spin-charge separation is obtained. The single-particle spectrum at half-filling is in accord with the recent angle-resolved photoemission spectrum in the 1D cuprate SrCuO 2 and is in strong contrast with that in the 2D one Sr 2CuO 2Cl 2. In 2D, the behaviors of these excitation spectra are strongly dependent on electron concentration. Far away from half-filling, the single-particle spectrum includes both spin and charge excitations as expected in a Fermi liquid. On the other hand, near half-filling, the spectra are rather similar to those in 1D, indicating that the spin and charge degrees of freedom obey the different dynamics. The spectra in a two-leg ladder are similar to those in 2D.

Renormalization Group Approach to the One–Dimensional 1/4–Filled Hubbard Model with Alternating on–Site Interactions

The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system, and to the dynamical generation of a gap in the charge excitation spectrum for Ua≠Ub, Ua>0 or Ub>0. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum, and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.

Absence of superconducting long-range order in low-dimensional Hubbard models

Using Bogoliubov's inequality we rigorously show that the one- and two-dimensional Hubbard model with narrow bands does not exhibit long-range order for different kinds of pairing, e.g. s-wave Cooper pairing and generalized η pairing. This result holds at any finite temperature for both repulsive and attractive Coulomb interactions. At zero temperature there will be no on-site electron pairing long-range order if a gap in the charge excitation spectrum exists. The present results do not cover the case of d x 2− y 2 pairing of electrons.