Calculated effects of charge fluctuations on the phonon dispersion of YBa2Cu3O6 and YBa2Cu3O7. I. The model

In this paper we present a microscopic model that allows us to study the effects of charge fluctuations on the phonon dispersion of the high-temperature superconductor YBa₂Cu₃O₇ and its insulating counterpart, YBa₂Cu₃O₆. An ab-initio rigid-ion model with pair potentials calculated by the Gordon-Kim method from the free-ion charge densities is used as a reference system. Starting from this reference system, charge fluctuations at the copper- and oxygen ions are introduced into the model. The charge fluctuations are treated as adiabatic degrees of freedom in a non-phenomenological way. The parameters entering the model are estimated consistently with the reference system from first principles rather than refering to the experimentally determined phonon dispersion. In addition to the metallic behavior (appropriate to YBa₂Cu₃O₇) obtained in this way, insulating behavior (appropriate to YBa₂Cu₃O₆) is simulated by requiring the polarizability function to fulfill a corresponding long. wavelength sum rule. Screened site-potential changes are defined that (besides the charge fluctuations) constitute a qualitative measure of the electron-phonon-interaction potential. Furthermore we investigate the long-wavelength limiting behavior of the most important quantities occurring in our formalism. We derive formulae that allow us to calculate the contribution of the charge fluctuations to the macroscopic dielectric constant and the transverse effective charges in the insulating phase.     

Non-superconducting and rendered superconducting YBa2Cu3O7−x . An in-situ photoemission study

We present X-ray photoemission spectroscopy (XPS) results obtained on polycrystalline YBa₂Cu₃O_7–x in the non-metallic (x>0.6) and metallic state (x<0.6) by an in-situ oxygen deloading/loading procedure, thus avoiding uncontrolled surface contaminations. The transition to the metallic (superconducting) state is characterized by corresponding changes in the O1s and Cu2p photoelectron lineshapes being in accordance with charge transfer from CuO₂ planes to CuO chains. In particular, a peak at 531.1 eV binding energy is related to the presence of oxygen hole states (O^–).     

Structure of grain boundaries in YBa2Cu3O7 thin-film step-edge junctions

The atomic structure of 90° [100] (or [010]) tilt grain boundaries in YBa₂Cu₃O₇ thin-film step-edge junctions and, for comparison, in the interface between a-axis and c-axis oriented YBa₂Cu₃O₇ grains is investigated by means of high-resolution transmission electron microscopy. For (100)(001)-type boundaries two different structures are found. In the first a (001) CuO₂ plane of one grain faces a (100) Y–Ba–O plane of the other grain, in the second a (001) BaO plane faces a (100) Cu–O plane. In the former structure an incomplete unit cell of YBa₂Cu₃O₇ terminates at the boundary and a smaller strain in the adjacent CuO₂ planes is detected in comparison with the latter. It is found that a combination of a partial dislocation with a 124 stacking fault is a way to accommodate the lattice mismatch between c and 3a of YBa₂Cu₃O₇ in the boundary. For a symmetric (103)(103)-type boundary a displacement of the Cu-atoms of the CuO₂ planes is found near the boundary plane. From this a redistribution of the oxygen atoms around the Y-atoms located right in the boundary plane is inferred. The possible effect of the boundary structure on the superconducting properties of YBa₂Cu₃O₇ films is discussed.     

Dielectric function of YBa2Cu3O7-δ between 50 meV and 50 eV

Electronic excitations with polarization parallel to the CuO₂-planes in single-crystalline YBa₂Cu₃O₇ and YBa₂Cu₃O₆ have been investigated by optical reflectance and by highenergy electron energy-loss spectroscopy in transmission in the energy ranges from 50 meV to 6 eV and 0.2 eV to 150 eV, respectively. From a combination of these experimental data the dielectric function, the reflectivity and the optical conductivity have been obtained in a wide energy range. The observed spectra are interpreted in terms of optical phonons, free-carrier absorption, transitions across the charge-transfer gap, further interband transitions, low-lying core-level excitations, excitonic transitions and valence conservingd-d transitions within the Cu 3d shell combined with O 2p intraband transitions. The charge carrier plasmon and the 4 eV-excitation in YBa₂Cu₃O₆ show quadratic dispersions in momentum transfer. From the dispersion constant of the plasmon a mean value of the Fermi velocity of the charge carriers parallel to the CuO₂ planes has been derived.     

Calculation of the electron-ion interaction-potential components linear and quadratic in the ion displacements for YBa2Cu3O7

A simple method is proposed to calculate the component of electron interaction potential with the ionic subsystem of a crystal quadratic in ionic displacement. The electron-ion interaction potential is calculated for the high-frequency A _g modes in YBa₂Cu₃O₇. The important role of the Madelung potential, which results in violation of the selection rules valid in the rigid muffin-tin approximation, is pointed out. The quadratic component of the potential can greatly affect the calculated matrix elements which correspond to electronic transitions involving absorption or emission of zero wave-vector phonons. Fiz. Tverd. Tela (St. Petersburg) 39, 1323–1327 (August 1997)     

In-plane polarized collective modes in detwinned YBa2Cu3O6.95 observed by spectral ellipsometry

The in-plane dielectric response of detwinned YBa₂Cu₃O_6.95 has been studied by far-infared ellipsometry. A surprisingly large number of in-plane polarized modes are observed. Some of them correspond to pure phonon modes. Others possess a large electronic contribution which strongly increases in the superconducting state. The free carrier response and the collective modes exhibit a pronounced a–b anisotropy. We discuss our results in terms of a charge density wave state in the 1-D CuO chains and induced charge density fluctuations within the 2-D CuO₂ planes.     

Cu nuclear spin-spin relaxation in YBa2Cu3O6.98 and YBa2Cu4O8

We have measured the temperature (T) dependence of the transverse relaxation rate (T _G ^–1 ) of the Cu(1) nuclear spin in YBa₂Cu₃O_6.98 (T _c=92 K) and YBa₂Cu₄O₈ (T _c=82 K). From the scaling ratio ofT _G ^–2 (Cu1) toT _G ^–2 (Cu2), we have estimated the strength of a covalent bonding between the CuO₂ plane and the CuO chain to be B0.38×A _zz. The experimentalT _G ^–1 (Cu1) in YBa₂Cu₄O₈ was of the same order of magnitude as the estimated one fromT _G ^–1 (Cu2). These results appear to indicate that the electrons in the CuO₂ plane fairly spread out of the plane in both compounds.     

Observation of the vortex-glass transition in YBa2Cu3O7 by phase-resolved current-voltage measurements

Abstract. We report on investigations of the current-dependent ac impedance Z at 17 Hz of a YBa₂Cu₃O₇ thinfilm microbridge in magnetic fields from 1 to 8 T. A phasesensitive lock-in technique was applied and supplemented by a pulsed method for high current densities. Above the vortex-glass transition temperature T _g a constant Z(j) is observed with low current densities j, and a power-law behavior at high currents. Below T _g, the curvature of the Re Z vs. j curve is negative in a log-log plot. The Re Z(j) isotherms can be collapsed onto two universal scaling functions according to the predictions of the vortex-glass model. Close to and below T _g, a phase lag between current and voltage appears, which saturates to finite values at low j and to zero at high j. The phase lag within the constant-Z(j) region remains below the critical value, predicted theoretically by Dorsey, if T > T _g and approaches 90° at T < T _g indicating the freezing of the vortices into the dissipation-free vortex-glass state.     

Effect of interlayer coupling in YBa2Cu3O7-y

The layered oxide superconductors are essentially two-dimensional in character with a weak coupling between copper oxide planes. Using perturbation arguments of scaling theory, we compare the scaling function in a quasi-two-dimensional layered material with that in a (2+) dimensional system and relate the interlayer coupling to an effective dimensionality. The effect of interlayer coupling on metallic conduction and superconductivity in YBa₂Cu₃O_7–y is discussed.     

Site of the positive muon in YBa2Cu3O7

A combination of μSR and¹⁷O nuclear quadrupolar μLCR has been used to obtain detailed information on the muon site in YBa₂Cu₃O₇. The rms magnitude of the nuclear dipolar fields in YBa₂Cu₃O₇ enriched with 38%¹⁷O is about twice that in the natural¹⁶O sample. In addition the¹⁷O μLCR spectrum shows that the electric field gradient tensor at the oxygen closest to the muon is almost equal to that measured by NMR for the CuO₂ plane sites O(2,3). These results suggest that the muon in fully oxygenated YBa₂Cu₃O₇ is located at a single site 1.0 Å from an oxygen ion, probably O(2,3).     

Micro‐Raman study of exfoliated Bi2Sr2CaCu2O8+δ single crystals with different thicknesses

Exfoliated Bi₂Sr₂CaCu₂O_8+δ (Bi‐2212) single crystals were prepared by micromechanical cleavage of bulk Bi‐2212 single crystals on SiO₂/Si substrates. Room temperature micro‐Raman spectra were collected using a 532‐nm laser source. The evolutions of the spectra of A_1g (Bi), A_1g (Sr), and A_1g (O_Bi) Raman modes with different thicknesses of the samples were studied. The refractive index of Bi‐2212 single crystal was obtained by studying the intensity evolutions based on the interference effect. The observed wavenumber shifts of the A_1g (Bi), A_1g (Sr), and A_1g (O_Bi) modes were analyzed. Copyright © 2011 John Wiley & Sons, Ltd.     

Renormalization of phonon frequencies by conduction electrons in layer systems with application to YBa2Cu3O7

It is generally assumed that there are free electronic carriers associated with the CuO₂ planes in high-temperature superconductors. Regarding these carriers as confined to these planes their influence on phonon frequencies is studied within the framework of a shell model of lattice dynamics taking into account the long-range part of the electron-phonon coupling. We find a complete suppression of the LO-TO splitting for modes polarized along the planes by metallic screening and a strong coupling of electronic plasmon and particle-hole excitations especially to some To-phonon branches polarized perpendicular to the conducting planes, particularly pronounced in systems with at least two CuO₂ planes per unit cell. Numerical results are presented for YBa₂Cu₃O₇.     

Lattice vibrations in the orthorhombic commensurate charge density wave phase of 2H-TaSe2

Lattice vibrations in 2H-TaSe₂ have been reinvestigated by Raman scattering in view of the recent orthorhombic structure of the commensurate charge density wave (CCDW) phase. The renormalization of six charge density waves on two layers gives four A_g modes and two B_1g modes in the orthorhombic CCDW phase, in place of two A_1g modes and two E_2g modes in the hexagonal CCDW phase which had been believed. The splitting of the E_2g modes to the A_g and B_1g modes in the orthorhombic symmetry depends on the interlayer interaction. The observed small splitting less than 3 cm^-1 shows the weak interlayer interaction. The energies of the four A_g modes and the two B_1g modes are presented as a function of temperature.     

Interface and grain boundary structures in YBa2Cu3O7-x and YBa2Cu4O8 materials

Y₂BaCuO₅YBa₂Cu₃O_7-x (Y211/Y123) interfaces in melt-processed YBa₂Cu₃O_7-x were studied by high-resolution transmission electron microscopy and energy dispersive X-ray spectroscopy. Yttrium enrichment and barium depletion were observed locally at the Y211/Y123 interfaces where Y123 (001) facets were present. This effect may be interpreted as the result of lattice substitution of Ba by Y near these interfaces. Cation nonstoichiometry was found near Y211/Y123 interfaces where liquid phases (Cu-Ba-O) were present. This chemical disorder introduces numerous point defects in the Y123, and these defects may act as additional pinning sites alongwith stacking faults. A comparison of grain boundary (GB) chemical composition in polycrystalline YBa₂Cu₃O_7-x and YBa₂Cu₄O₈(Y124), studied using nanoprobe parallel-detection electron energy-loss spectroscopy (EELS), is presented. The studies of Y124 show that stoichiometric grain boundaries can also form weak links between superconducting grains. It is suggested that weak-link behavior is determined largely by misorientation at grain boundaries.     

Influence of interatomic forces on the lattice dynamics of YBa2Cu3O7 (molecular dynamics method)

The method of molecular dynamics is used to study the dynamic properties of the high-temperature superconductor YBa₂Cu₃O₇. It is shown in the system La_2−x Sr_xCuO₄ that, due to the presence of strong anharmonism and a substantial difference in the interatomic forces, local “hot” regions arise around the Ba⁴⁺ charge defects in the CuO₂ and CuO planes, where the mean kinetic energy of the vibrations of the oxygen atoms reaches ∼0.5 eV. All other types of defects: oxygen and copper vacancies, substitutional atoms, and charge defects, do not lead to such effects. Fiz. Tverd. Tela (St. Petersburg) 41, 1729–1733 (October 1999)     

Dynamics of the superconducting mixed state in YBa2Cu3O7-δ/PrBa2Cu3O7-δ superlattices in radio frequency regime

Epitaxial multilayers of YBa₂Cu₃O_7-δ and P₁Ba₂Cu₃O_7-δ have been deposited on (100) cut SrTiO₃ substrates using the technique of pulsed laser deposition. Standard ϑ-2ϑ X-ray diffraction measurements on the films showed excellent superlattice reflections. The mixed state of these superlattices has been probed through measurements of radio frequency penetration depth (λ) as a function of temperature (T), magnetic field (H) and it’s orientation (ϑ) with respect to the planes of the superlattices. These data reflect the two-dimensional nature of the mixed state in these systems.     

Shape of the Cu(2) NQR spectra in YBa2Cu3O7, TmBa2Cu3O7 and TmBa2Cu4O8

We present a study of shape of the Cu(2) NQR spectra in YBa₂Cu₃O₇, TmBa₂Cum₃O₇, and TmBa₂Cu₄O₈ compounds at temperatures of 4.2–300 K. The results of the quantitative analysis lead us to conclude that the shape of the Cu(2) NQR spectra in all the samples studied can be described in the framework of the “motional narrowing” model, which implies that the Cu(2) nucleus possesses two different NQR frequencies between which it can rapidly jump. The difference in frequencies seems to be related to the charge-stripe correlations in CuO₂ planes resulting in a dynamical modulation of the electric field gradients at the Cu(2) nuclei. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 594–598 (10 November 1997)     

Electronic properties of YBa2Cu4O8 and Y2Ba4Cu7O15 as probed by NMR/NQR

Nuclear Magnetic Resonance (NMR) and Nuclear Quadrupole Resonance (NQR) allow the investigation of electronic properties at the atomic level. We will report on such studies in typical members of the Y-Ba-Cu-O family of high-temperature superconductors, namely YBa₂Cu₄O₈ and Y₂Ba₄Cu₇O₁₅. We will deal with temperature and orientational dependences of Cu and O Knight shifts and spin-lattice relaxation. Topics to be discussed are: (1) Existence of a common electronic spin-susceptibility (a single-spin fluid) in the planes and in the chains of YBa₂Cu₄O₈. (2) Evidence for the existence of a pseudo spin-gap in the anti-ferromagnetic fluctuations in YBa₂Cu₄O₈ and Y₂Ba₄Cu₇O₁₅. (3) Evidence for non-s symmetry of the pair wave function in YBa₂Cu₄O₈. (4) First NQR observation of a strong coupling of inequivalent Cu-O planes in Y₂Ba₄Cu₇O₁₅. (5) Alternative explanations of relaxation and Knight shift.     

Vortex-creep activation energy in YBa2Cu3O7/PrBa2Cu3O7 superlattices

YBa₂Cu₃O₇/PrBa₂Cu₃O₇ (YBCO/PBCO) superlattices with a different ratio of the superconducting and insulating layer thicknesses were prepared by high pressure dc sputtering. The vortex-creep activation energy U₀ was determined by analyzing the in-plane resistive transition of 200 μm wide bridges with the external magnetic field B oriented along the c axis. It was found that U₀ is proportional to the thickness of the YBCO layers, and does only weakly depend on the PBCO layer thickness, when the latter exceeds two unit cells. We observed a change in the variation of U₀ with the current I in the specimen: U₀ exhibits a plateau in the low-I region, then decreases significantly with increasing I. This behaviour is explained in terms of a crossover plastic vortex creep – elastic (collective) creep induced by the transport current.     

Optical control and mode selective excitation of coherent phonons in YBa2Cu3O7−δ

Femtosecond time-resolved reflectivity measurement is performed on Y Ba₂Cu₃O_7?δ films. Coherent phonons of both the Ba–O and Cu–O modes are observed at frequencies of 3.4 and 4.3 THz, respectively. Amplitudes of both Ba–O and Cu–O modes are optically manipulated by using a pair of femtosecond pulses, the separation time of which is controlled. Coherent phonons of the Ba–O and Cu–O modes are completely suppressed at the double-pulse separation times of 135.0 and 108.5 fs and those amplitudes are enhanced at 270 and 217 fs, respectively.