Oxygen Breathing Mode Research Articles

Screening and Phonon-Plasmon Scenario as Calculated from a Realistic Electronic Bandstructure Based on LDA for La2CuO4

The investigations performed in this work primarily deal with the question whether or no phonon-plasmon coupling along the c-axis in metallic La 2 CuO 4 will occur in case a realistic electronic bandstructure based on the local density approximation (LDA) is employed for the calculation of the electronic polarizability II and the dielectric matrix e. Phonon-plasmon mixing will appear in a significant way if the frequency of the free, uncoupled plasmon, as determined from the zeros of the dielectric matrix e, will fall into the frequency range of the phonon modes of appropriate symmetry coupling to the plasmon. For such a possibility to arise the dispersion of the electronic bandstructure along the c-axis must be sufficiently weak (small bandwidth). Qualitatively, we recently have studied phonon-plasmon mixing by using an 11-band tight binding model for the electronic bandstructure of the CuO plane, while the electronic bandstructure along the c-axis was introduced from the outside applying suitable interlayer couplings in parametrized form. In the present calculation the electronic bandstructure employed for the calculation of n and e, respectively, results from a complete tight-binding representation of the first-principles LAPW data including La 5d, Cu 3d, 4s, 4p and O 2p states (31-band model). No additional assumptions concerning the interlayer coupling are introduced in contrast to the 11-band model. Besides the nonadiabatic regime along the Λ∼(0, 0, 1) direction where dynamical screening and phonon-plasmon mixing comes into play, the phonon dispersion is also calculated for the main symmetry directions using the adiabatic approximation, i.e. assuming static screening. Besides other features, from this calculation the growing importance of the itinerant component of the charge response in the CuO plane to achieve high-T c values can be extracted. The charge fluctuations and the self-consistent changes of the crystal potential at the ion sites as induced by the symmetrical apical oxygen breathing mode at the Z point (O Z z ), being important for nonlocal electron-phonon interaction and pair binding, are calculated for the phonon-like and plasmon-like modes. Furthermore, a comparison is made with recent inelastic neutron scattering results for certain phonon anomalies. Finally, a possible solution concerning the apparent inconsistency of the current interpretation of the neutron c-axis data with the infrared c-axis optical spectra in La 2 CuO 4 is shortly outlined. Based on this discussion, the possibility for the application of a typical (LDA) bandstructure result for the description of the c-axis response in LaCuO the other HTSCs is estimated.

A Raman spectroscopic investigation of methoxyl end capped PPO doped with NaCF 3SO 3

Raman spectroscopy was used to study ionic association and polymer conformation in methoxyl end capped PPO (M–PPO) doped with NaCF 3SO 3, for temperatures ranging from 230–340 K. M–PPO of molecular weights 400 to 2000, pure and doped with sodium triflate of concentration O:M=15:1, were studied in order to investigate the importance of the end groups for ionic solvation. It is found that in M–PPO, in contrast to OH-terminated PPO, the number of dissociated ions is independent of molecular weight. Moreover, the ion-association in the M–PPO systems was found to be comparable to that reported for OH–PPO of molecular weight 4000 indicating that the latter is an excellent low molecular analogue to higher molecular weight systems. Furthermore, the absence of a distinct polarised metal–oxygen breathing mode in the M–PPO salt complexes indicates a polymer–ion interaction different from the symmetric configurations of chains wrapped around cations as suggested for PEO based polymer electrolytes. The solvation model of cations forming cross-links via coordinations to ether oxygens of adjacent chains is favoured.

Linked four-membered silicate rings: vibrational analysis of Gillespite

Raman spectra and lattice dynamics calculations are presented for the silicate mineral gillespite, BaFeSi4O10, which contains sheets of linked four-membered silicate rings. The results are analyzed in relation to earlier work done on the isolated four-membered ring silicate BaCuSi2O6 and to published claims that vibrational modes of four-membered rings are responsible for the sharp D 1“defect line” observed in the Raman spectra of SiO2 glass. The crystal structure of gillespite (space group P4/ncc or D ) consists of puckered Si4O12 rings, where each SiO4 tetrahedron is linked to two neighboring tetrahedra within a ring and to a third tetrahedron within a different ring. The rings are linked to each other in a staggered configuration to form sheets, which are also bonded together by Ba2+ and Fe2+. The calculation adjusts the bond bending and bond stretching force constants so that calculated fundamental mode frequencies best fit observed fundamental frequencies in the Raman spectra; eigenmodes associated with each calculated fundamental mode are then generated. Some eigenmodes calculated are unique to the gillespite structure, but many of the more localized four-membered ring modes are similar to those calculated for the four-membered rings in BaCuSi2O6 and for the three- and six-membered rings in the cyclosilicates studied earlier. The results for gillespite indicate that the Raman-active A 1g mode at 450 cm−1 is a four-membered ring bridging oxygen breathing mode that is mixed with other minor ring deformation displacements; because of this mixing, the calculated frequency of this mode is 45 to 61 cm−1 lower than that calculated for bridging oxygen binding breathing modes of puckered four-membered rings in BaCuSi2O6 and in simulated glass structures.

Stripes, pseudogaps, and Van Hove nesting in the three-bandt-Jmodel

Slave boson calculations have been carried out in the three-band tJ model for the high-T_c cuprates, with the inclusion of coupling to oxygen breathing mode phonons. Phonon-induced Van Hove nesting leads to a phase separation between a hole-doped domain and a (magnetic) domain near half filling, with long-range Coulomb forces limiting the separation to a nanoscopic scale. Strong correlation effects pin the Fermi level close to, but not precisely at the Van Hove singularity (VHS), which can enhance the tendency to phase separation. The resulting dispersions have been calculated, both in the uniform phases and in the phase separated regime. In the latter case, distinctly different dispersions are found for large, random domains and for regular (static) striped arrays, and a hypothetical form is presented for dynamic striped arrays. The doping dependence of the latter is found to provide an excellent description of photoemission and thermodynamic experiments on pseudogap formation in underdoped cuprates. In particular, the multiplicity of observed gaps is explained as a combination of flux phase plus charge density wave (CDW) gaps along with a superconducting gap. The largest gap is associated with VHS nesting. The apparent smooth evolution of this gap with doping masks a crossover from CDW-like effects near optimal doping to magnetic effects (flux phase) near half filling. A crossover from large Fermi surface to hole pockets with increased underdoping is found. In the weakly overdoped regime, the CDW undergoes a quantum phase transition ($T_{CDW}\to 0$), which could be obscured by phase separation.

Origin of phonon anomalies inLa2CuO4

The experimentally observed softening of the oxygen breathing mode at the X point, ${\mathrm{O}}_{\mathrm{X}}^{\mathrm{B}}$, and of a second CuO bond stretching mode of ${\mathrm{\ensuremath{\Delta}}}_{1}$ symmetry at the wave vector q=(0.5,0,0) in the doped metallic phase of La-Cu-O is investigated and shown to be driven by long-range, nonlocal electron-phonon interaction effects of monopole charge-redistribution type. The amplification of softening for both modes by about 1 THz, recently found in inelastic neutron scattering for an optimally doped ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_{4}$ probe as compared with an underdoped ${\mathrm{La}}_{1.9}$${\mathrm{Sr}}_{0.1}$${\mathrm{CuO}}_{4}$ crystal is explained by the growing importance of the more extended orbitals in the charge response in particular at the Cu ion. Such an enlarged contribution of the more extended orbitals leads to a reduction of the dominant self-interaction, U, of the electrons mainly at the Cu and allows for an enhancement of the monopole charge redistributions whose magnitude determines the softening of the phonon modes. The existence of a specific mixture of localized and more extended states at the Fermi energy is crucial for the appearance of the strong nonlocal electron-phonon coupling of ionic origin and for the reinforcement of the phonon mediated part of pairing in the high-temperature superconductors.

Aspects of the normal-state phase of copper oxide planes in high-Tc superconductors.

We examine various aspects of the normal-state phase of Cu${\mathrm{O}}_{2}$ planes in the high-${T}_{c}$ superconductors. In particular, within the context of the three band Hubbard model, we study as a function of doping the competition between a charge density wave phase induced by oxygen breathing modes, antiferromagnetic order, and paramagnetism. To account for the strong electronic interactions, we use the finite $U$ slave boson method of Kotliar and Ruckenstein.

Vibrational analysis of wadeite K2ZrSi3O9 and comparisons with benitoite BaTiSi3O9.

Raman scattering measurements and lattice dynamics calculations are reported for the cyclosilicate mineral wadeite K2ZrSi3O9 . The structure of this crystal ~space group P6 or C 3h 1 ! consists of planar three-membered silicate rings ~Si3O9! linked by K 1 and Zr 41 ions. The rings in wadeite are nearly identical to those in the mineral benitoite BaTiSi3O9 . The wadeite structure differs from that of benitoite, however, in that the rings are in a staggered configuration, rather than arranged one directly above the other in columns. The calculation reported here employs a valence force potential consisting of central interactions between nearest neighbors and bond-bending interactions centered at the K 1 ,Z r 4 1 ,S i 4 1 , and O 22 ions, with force constants determined by fitting the frequencies observed in the Raman spectra. The calculation is in reasonable agreement with experiment, permitting assignment of normal modes to the observed spectral frequencies. Considerable mixing of K 1 and Zr 41 motions with those of the rings is found for Raman-active modes below 250 cm 21 . The highly localized normal modes of the planar three-membered silicate rings in wadeite are nearly identical to those determined for the rings in benitoite, at frequencies above 800 cm 21 . At lower frequencies, however, the similarities become less obvious as internal ring modes can be mixtures of idealized three-membered ring modes that are unique to each mineral. A striking result in the case of wadeite is the absence of the bridging oxygen breathing mode that was found for benitoite and two other cyclosilicates studied previously. This finding may have consequences for the interpretation of the Raman spectra of silicate glasses, since a breathing mode of this type has been postulated to be a universal feature of networks containing three-membered rings. @S0163-1829~96!07621-7#

Interplay of charge and spin correlations in nickel perovskites

Analyzing the motion of low-spin (s=1/2) holes in a high-spin (S=1) background, we derive a sort of generalized t-J Hamiltonian for the NiO2 planes of Sr-doped nickelates. In addition to the rather complex carrier-spin and spin-spin couplings we take into account the coupling of the doped holes to in-plane oxygen breathing modes by a Holstein-type interaction term. Because of strong magnetic confinement effects the holes are nearly entirely prelocalized and the electron-phonon coupling becomes much more effective in forming polarons than in the isostructural cuprates. In the light of recent experiments on La2−xSrxNiO4 we discuss how the variety of the observed transport and charge/spin-ordering phenomena can be qualitatively understood in terms of our model Hamiltonian.

Bismuth disproportionation inBaBiO3studied by infrared and visible reflectance spectra

${\mathrm{BaBiO}}_{3}$, the end member of the system (Ba,K)(Pb,Bi)${\mathrm{O}}_{3}$, raises a number of problems that are interesting to study as a step towards the understanding of superconductivity in certain compounds of the series. Using infrared and visible reflectivity spectroscopy, the thermal evolution of the reflectance of a ${\mathrm{BaBiO}}_{3}$ single crystal is reported, analyzed, and compared to an oxygen-deficient sample. Oxygen effective charges are also evaluated. The results are discussed within the framework of possible bismuth disproportionation and its consequences in terms of bismuth-oxygen distances, crystal symmetry, oxygen breathing mode, charge density wave, opening of a gap at the Fermi energy, or polaron formation.

Phonon renormalization and c-axis phonon-plasmon mixing in La2CuO4.

A decomposition of the electronic-density response recently worked out for the description of local, nonlocal, and nonadiabatic electron-phonon interaction effects in the high-temperature superconductors is applied to the lattice dynamics and phonon-plasmon mixing in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. The local part of the density response and the electron-phonon interaction is approximated by an improved model of rigid ions using effective ionic charges as calculated from a tight-binding analysis of the first-principles electronic band structure. Moreover, covalence effects are simulated by scaling the short-range part of the relevant ab initio pair potentials. Such a model serves as a reference system describing the insulating phase. Phonon dispersion curves are calculated in this model and good overall agreement with recent experiments is found. In the case of the metallic phase, specific nonlocal screening effects in terms of localized charge fluctuations are additionally introduced at the ions by a parameter-free procedure. In the framework of the improved reference system, phonon dispersion curves and phonon-induced changes of the crystal potential are calculated for the metallic phase. Characteristic changes in the phonon dispersion produced by the insulator-metal transition are discussed and compared with the experiments. Further, c-axis phonon-plasmon mixing is investigated. Phonon-plasmon coupling leads in particular to an additional softening of the symmetrical apical oxygen breathing mode at the Z point (${\mathit{O}}_{\mathit{Z}}^{\mathit{z}}$) being important in context with nonlocal electron-phonon interaction and pair binding. In this way the already large decrease in frequency of this phonon predicted in our earlier work in the adiabatic approximation as compared to the calculated frequency of ${\mathit{O}}_{\mathit{Z}}^{\mathit{z}}$ in the insulating phase is further enhanced. The anomalous large renormalization of this mode has been confirmed quite recently by the experiments. A final remark is concerned with the oxygen isotope effect in the high-temperature superconductors from the viewpoint of phonon-plasmon coupling.

Electron-phonon coupling and d-wave superconductivity in the cuprates.

We derive an effective single-band Hubbard-type Hamiltonian for ${\mathrm{CuO}}_{2}$ planes in the cuprate high-${\mathit{T}}_{\mathit{c}}$ superconductors. The Hamiltonian includes both electron-electron repulsion and electron-phonon coupling to oxygen vibrational modes. The effective Hamiltonian is derived by mapping from the multiband constrained-density-functional-theory Hamiltonian to a one-band model. A Hartree-Fock mapping leads to t=0.66 eV, t'=-0.14 eV, and U=4.0 eV. Very similar parameters are obtained by exact diagonalization of finite clusters. The electron-phonon coupling to oxygen breathing modes gives \ensuremath{\lambda}=0.57 for s-wave and \ensuremath{\lambda}=0.35 for ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ pairing. d-wave superconductivity is predicted to occur at 30 K for doped ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, while the strong Coulomb repulsion suppresses the s-wave ${\mathit{T}}_{\mathit{c}}$ to 10 K.

T c Enhancement by local oxygen breathing modes in Ba( Pb, Bi) O3

Calculations of the electron-photon interaction in Ba( Pb, Bi) O 3 alloys are presented for a variety of 2 × 2 × 2 supercell configurations. Strong deviations from the virtual crystal approximation are found, leading to enhanced e-ph coupling, mainly by local O ‘breathing’ modes around the Bi atoms.

Effective single-band Hamiltonian for electron-phonon coupling in cuprate superconductors

We derive an effective single-band Hubbard type Hamiltonian for CuO2 planes. The Hamiltonian includes both electron-electron repulsion and electron-phonon coupling to oxygen vibrational modes. We start with first-principles density functional theory parameters and then map onto a single-band model. Unlike previous mappings to a single-band Hamiltonian, ours explicitly preserves the Fermi surface shape and matrix elements of the many-band Hamiltonian. We consider both in-plane oxygen breathing modes as well as out-of-plane tilting modes. The latter modes have a quadratic electron-phonon coupling, and are also highly anharmonic in La2CuO4 based superconductors. The coupling to breathing modes is too small to account for highTc, while the coupling to quadratic modes is much stronger even though they would be neglected in a standard Migdal-Eliashberg approach to superconductivity.

Explanation of the temperature dependence of resistivity in high- Tc superconducting Ba 0.6K 0.4BiO 3 by electron-phonon scattering

The resistivity ϱ( T) of single crystals of the cubic high- T c superconductor Ba 0.6K 0.4BiO 3 with T c=30 K has been measured in the temperature range from 4.2 to 300 K. The experimental curve is well approximated in the framework of the classical electron-phonon model of resistivity by the Grüneisen type dependence using the phonon spectrum in the form of an acoustic branch and a widely separated narrow optical peak. Characteristic temperatures of the phonon spectrum — the Debye temperature Θ D of the acoustic branch and the Einstein temperature Θ E of the optical mode — and the ratio of contributions of acoustic and optical phonons to the resistivity were derived from the best fit of the theoretical curve ϱ( T) to the experimental one. The optical phonons of the oxygen breathing mode give a relatively larger contribution to the resistivity. Correspondingly, the contribution of optical phonons to the constant of electron-phonon interaction λ is larger compared to the contribution of acoustic phonons.

Effect of charge fluctuations on the phonon dispersion and electron-phonon interaction in La2CuO4.

In this paper we propose a formulation of the electronic density response that is well suited to investigate the influence of localization and delocalization properties of the electrons on the phonon dispersion and the electron-phonon interaction. The formalism is applied to study nonlocal, long-range, electron-phonon-interaction effects of the charge-fluctuation type in high-temperature superconductors, using ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ as an example. Some important features in the experimental phonon spectrum can be understood within such an approach. We discuss the modification of the usual picture of electron pairing, taking into account these nonlocal effects. In this context the symmetric apical oxygen breathing mode at the Z point is of special importance. In this vibration, nonlocal electron-phonon-interaction effects of the charge-fluctuation type are shown to generate in the metallic phase of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ an interplane charge transfer that is blocked completely in the insulating phase if a strictly two-dimensional electronic structure is assumed. Very recently we became aware of unpublished experimental results where this previously undetected mode appears, unusually broad, as the highest ${\mathrm{\ensuremath{\Lambda}}}_{1}$ mode at the Z point, in agreement with our theoretical predictions for the insulating phase. Finally, our considerations point towards a simple structure that could be very effective for high-temperature superconductivity.

Molecular orbital calculations of vibrations in three-membered aluminosilicate rings

Ab initio, molecular orbital calculations at the 3–21G* level were carried out on H6Si3O9, [H6Si2AlO2]1−, [H6SiAl2O9]2−, and [H6A13O9]3− cyclic molecules in order to determine their structures and vibrational frequencies. These three-membered rings were found to have minima in their potential energy surfaces indicating stability of the species. The H6Si3O9 ring was found to be slightly non-planar, but the [H6SiAl2O9]2− and [H6Al33O9]3− configurations are more planar. Vibrational frequencies of the Raman-active, bridging oxygen “breathing” modes increase with Si4+ content. Galeener's (1982a, b) assignment of the D2 peak (606 cm−1) in the Raman spectrum of vitreous silica to an oxygen breathing mode in rings of three SiO4 tetrahedra is reconfirmed. Correlation of the ring breathing mode frequencies as a function of (AI/AI + Si) with Raman peaks in the SiO2-NaAlSiO4 system is high. Three-membered aluminosilicate rings are likely to exist and give rise to Raman peaks between 540 and 600 cm−1 in fully-polymerized aluminosilicate glasses.

Phonon softening in ceramic superconductors

The phonon density-of-states of the ceramic superconductors Ba 0.6K 0.4BiO 3, BaPb 0.75Bi 0.2O 3 and BaPb 0.75Sb 0.25O 3 has been measured by the neutron time-of-flight technique to very low energy transfer. Measurements on metallic BaPbO 3 and semiconducting BaBiO 3 are also reported. Phonon anomalies, associated with high-frequency oxygen breathing modes are observed. The low-frequency region also reveals additional features that vary across the series. The results are consistent with phonon-mediated mechanisms for superconductivity.

Anisotropic screening of oxygen polarizabilities: a scenario to understand superconductivity in oxides

The highly anharmonic motion of apical oxygen in a double-well potential, related to its large unscreened polarizability, in an oxygen breathing mode configuration, enhances the electron-phonon coupling to produce high critical temperature superconductivity. It also explains the weakness of the isotope effect. Available experimental data, mainly from IR and neutron experiments, which are relevant to this mechanism are discussed.

Electronic States and Metal-Semiconductor Transition in BaPb1-xBixO3

The electronic structure of BaPb 1- x Bi x O 3 (BPB) is calculated in the framework of mean field approximation and coherent potential approximation, describing the electronic motion in terms of the extended Hubbard model with two kinds of site-dependent parameters; difference in the on-site energies on Bi and Pb sites and effective on-site interaction due to the oxygen breathing modes. Three characteristic band-shapes are obtained as a function of Bi concentration x ; a single band and pseudo-gapped band for metallic phase and two separated bands for semiconducting phase, indicating that x plays a role similar to that of the temperature in the case of the Peierls instability. These results are successfully applied to interpret the main features of metal-semiconductor transition of BPB obtained from optical spectra.

Valence fluctuations in the (yttrium barium copper oxide), YBa2Cu3O7-x superconductor

The electronic structures of copper oxide clusters representing the new superconducting materials YBa/sub 2/Cu/sub 3/O/sub 7-x/ and La/sub 2-x/M/sub x/CuO/sub 4/ (M = Ba, Sr) have been calculated by semiempirical molecular orbital methods. For YBa/sub 2/cu/sub 3/O/sub 7-x/ the orbital energies indicate that the Cu's located in the CuO/sub 3/ chains are primarily trivalent, while the Cu's in the CuO/sub 2/ dimpled planes are primarily divalent. The effects of the oxygen breathing mode on the charge distributions and orbital energies are investigated for different electronic configurations. The results indicate that the oxygen breathing modes can cause significant charge fluctuations on the Cu's in the clusters. For certain electron configurations, a double-well type potential may exist for oxygen movement between Cu's in the chains. This may cause an instability at oxygen stoichiometries near 6.75 and result in a phase separation. A phase diagram is proposed for YBa/sub 2/Cu/sub 3/O/sub 7-x/, which suggests that the 94 K high-temperature superconducting phase is characterized by an oxygen stoichiometry near 7.0. The phase diagram predicts that a plateau should exist for T/sub c/ in the region x = 0.0-0.25 and that in this region two phases are present which are characterized by compositions having oxygenmore » stoichiometries either in the range 6.5-6.75 or close to 7.0. 24 refs., 5 figs., 4 tabs.« less