Low Temperature Anharmonicity and Superconductivity in Cuprates

Temperature-dependent X-ray absorption spectra of the hole-doped La_2?x Sr _x CuO₄ and electron-doped Nd_2?x Ce _x CuO_4?δ high-temperature superconductors were investigated above the Cu K absorption edge. We observed strong anharmonicity in the superconductive CuO₂ plane. For x=0.15 it was shown that part of oxygen ions oscillate in a double-well potential and their vibrations are correlated with the local electron (hole) pair transfer. We suppose that at a low temperature the phase coherence of the local pair movement is determined by the peculiarities of the perovskite-like structure which includes the stiff CuO _n (n=4,6) complexes combined by collective rotational and breathing modes.     

c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

Non-linear Localized Lattice Mode Coupling Mechanism and the Pseudogap in High-temperature Superconducting Cuprates

The pseudo-gap phenomena in high-temperature cuprate superconductors is an outstanding puzzle with no consensus yet on its physical origin. A previous suggestion on the role of non-linear local lattice instability modes on the microscopic pairing mechanism in high temperature cuprate superconductors is re-examined to investigate whether unusual lattice mechanisms could cause a pseudo-gap. By assuming an electron predominantly interacting with a non-linear Q ₂ mode of the oxygen clusters in the CuO₂ planes, we show that the interaction has explicit d-wave symmetry and leads to an indirect coupling of d-wave symmetry between electrons. We show that the polaron formation by the non-linear mode can cause a pseudo-gap of d-wave symmetry before the onset of coherence in the superconducting pairing. We suggest a simple phenomenological explanation of the pseudo-gap crossover temperature and the Fermi arcs. The discussion may be relevant for the pseudo-gap in non-superconducting giant magnetoresistive manganites.     

c-axis phonons and the enhancement of pairing correlations in high-temperature superconductors

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U→∞ limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO₂ layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureT _c. Our model calculation demonstrates that a pronounced enhancement ofT _c in thed-wave channel is possible. The largest enhancement ofT _c tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.     

Roles of oxygen defects in copper oxide superconductors

Oxygen vacancy and interstitial defects can have a profound effect on the superconducting properties of copper oxide compounds. Recent work on compounds such as La₂CuO_4+x and HgBa₂CuO_4+x has provided new insight into the role of interstitial oxygen defects as a doping mechanism. The number of carriers created by each interstitial defect depends on the local defect structure. Studies of (La, Sr, Ca)₃Cu₂O_6+x with various metal compositions and metalsite ordering show that interstitial oxygen defects that form between the CuO₂ layers in this structure systematically lowerT _c and eventually destroy superconductivity. Conversely, oxygen vacancies in the CuO₂ planes have surprisingly little effect at concentrations below 3%. The infinite-layer compounds, ACuO₂, where A=La, Sr, Ca, Nd, etc., in solid-solution combinations, could offer a similar environment for the formation of interstitial oxygen defects between the CuO₂ planes, allowing interstitial oxygen defects to contribute to the doping of these compounds. However, neutron diffraction experiments on Sr_0.9La_0.1CuO₂ (T _c = 42 K) have not found any interstitial oxygen.     

Structural and transport properties of the layered cuprate Pr<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

The structural and transport properties of the layered cuprate Pr₂CuO₄ have been studied in the temperature range 300–2100 K using molecular dynamics simulation. The first evidence is presented for a premelting effect in Pr₂CuO₄: disordering on one of its oxygen sites and abnormally fast oxygen diffusion at temperatures above 1700 K. We have clarified the microscopic mechanism of oxygen ion transport in this material. The large oxygen diffusion coefficient (D > 10⁻⁷ cm²/s) obtained in our simulations of the layered cuprate Pr₂CuO₄ suggests that it has considerable potential as a host for electrode materials with mixed ionic-electronic conductivity.     

Cd-Doped Cu0.5Tl0.5Ba2Ca2Cu3?yCdyO10?δ (y=0,0.5,1.0,1.5,2.0) Superconductors

Superconducting properties of cadmium doped Cu_0.5Tl_0.5Ba₂Ca₂Cu_3−y Cd _y O_10−δ (y=0,0.5,1.0,1.5,2.0) samples have been studied using X-ray diffraction, resistivity, ac-susceptibility and FTIR absorption measurements. In X-ray diffraction studies these samples have shown to have tetragonal structure. The zero resistivity critical temperature and magnitude of diamagnetism are suppressed with the increased incorporation of Cd in the final compound. A change in the shape of FTIR absorption spectra, after doping, has shown the incorporation of Cd in the unit cell. A systematic hardening of the apical oxygen modes and softening of the CuO₂ planar modes of vibration with increased Cd doping have shown that it is incorporated in the unit cell of Cu_0.5Tl_0.5Ba₂Ca₂Cu_3−y Cd _y O_10−δ (y=0,0.5,1.0,1.5,2.0) superconductors. The FTIR absorption measurements of these samples have shown that hardening of the apical oxygen modes of types Cu(1)–O(2)–Tl and Cu(1)–O(2)–Cu(2)/Cd _y (y=0,0.5,1.0,1.5,2.0) increases with the increase of Cd doping in the samples. A softening of the CuO₂ planar oxygen mode Cu(2)–O–Cu(2) is also observed with the increased Cd doping in the final compound. It is most likely that hardening of the apical oxygen modes and the softening of the planar modes of vibration are associated damped harmonic oscillations produced by heavier Cd atoms in the CuO₂ planes, which suppress the phonon population from a desired level, reducing the magnitude of superconductivity in the final compound.     

Electron spin resonance studies of some cuprate(II)systems

The electron spin resonance (ESR) of a number of ternary oxides of copper (II) has been studied at both 77 K and 300 K. Materials investigated include those which might be considered 1-dimensional analogues of La₂CuO₄, namely A₂CuO₃ (A=Ca,Sr, Ba) plus the related material SrCuO₂. The two oxygen rich derivatives of Ba₂CuO₃ have also been studied in view of their different oxygen environments around copper. Also other alkaline earth cuprates such as the recently described Sr₁₄Cu₂₄O_41-x and Bi₂Cu₂O₅, both pure and doped with Sr²⁺ are included. Compounds containing extended Cu-O chains are found to be essentially ESR silent both at room temperature and 77 K, regardless of whether the chains are one-dimensional or form two-dimensional sheets as in Ca(Sr)CuO₂. In Sr₁₄Cu₂₄O_41−x , which contains both Cu-O chains and chains of edge-shared CuO₄ square-planar units there is an asymmetric signal which sharpens on cooling.     

On the oxygen isotope shift in La2?xSrxCuO4

The anomalous oxygen isotope shift observed in the high-temperature superconductors La_2–xSr_xCuO₄ and La_2–xBa_xCuO₄ is discussed within the model of superconductivity in which the apex oxygen vibrations play the major role in the pairing mechanism. We show that the dependence of both the critical temperature and its isotope shifts on the doping level is consistently described within this model. The anomaly occurring in the isotope shift between x = 0.11 andx=0.15 is traced back to the oxygen mass exponent associated with the apex oxygen frequency.     

Single Crystals of HgBa2Can-1CunOx and Chain Compounds A1-xCuO2 (A=Sr, Ca, Ba), High Pressure Synthesis and Properties

High gas pressure up to 11 kbar has been applied for the synthesis and single crystal growth of Hg-based superconductors and one-dimensional A _1-x CuO ₂ cuprates. We have investigated the influence of Re, Sr and Pb substitutions and oxygen content on the magnetic flux-pinning properties of single crystals of Hg-based superconductors. The best results have been obtained for Sr and Pb substituted Hg1223 single crystals. Susceptibility, neutron scattering, and torque investigations have been performed on Ca _0.83 CuO ₂ , Sr _0.73 CuO ₂ and Ba _0.67 CuO ₂ compounds containing CuO ₂ infinite chains separated by Ca, Sr or Ba layers.     

Structural instabilities and superconductivity in La-214 compounds

In La_2–x Ba _x CuO₄ (LBCO) the transition to a low-temperature tetragonal phase and the suppression of superconductivity occur at the carrier concentration p 1/8 per copper. We will discuss the roles of various material parameters that control this instability. An unusual lattice softening has been found by ultrasonic measurement on La_2–x Sr _x CuO₄ (LSCO). This softening is present only in an in-plane shearing mode and is ascribed to the growth of structural fluctuations in the normal state.These phenomena are closely related because both the structural change in LBCO and the applied strain in LSCO lift the degeneracy of in-plane oxygen sites. They clarify the importance of strong coupling between the normal-state electronic system and the lattice by a Peierls-type mechanism.     

Tilting Mode Relaxation and Oxygen Isotope Effect in La2?xSrxCuO4 Studied by Electron Paramagnetic Resonance

The electron paramegnetic resonance (EPR) of Mn²⁺ doped into La_2–x Sr _x CuO₄ was used to probe the copper spin relaxation via the bottleneck effect for oxygen isotope (¹⁶O and ¹⁸O)–substituted samples. It was found that the EPR linewidth is larger for the ¹⁸O isotope samples than for the ¹⁶O samples. For x = 0.03, the linewidth for the ¹⁸O sample is larger than for ¹⁶O sample by a factor of 2. The isotope effect is pronounced at low temperatures and decreases with increasing Sr concentration. This effect is quantitatively explained by the Cu²⁺ S = 1/2 spin relaxation to the lattice via Dzyaloshinski terms coupled linearly to the local Q ₄/Q ₅ tilting modes of the CuO₆ octahedra as proposed by Kochelaev et al. [1] The Q ₄/Q ₅ modes are coupled sterically to the Q ₂ Jahn–Teller modes considered to be relevant for the (bi)-polaron formation and thus for the high-temperature superconductivity (HTSC).     

Existence of boths andd-wave solutions of Eliashberg equations

We solve Eliashberg equations in the case of strong anisotropic electron-phonon coupling and low energy cutoff. In a simplified model representing the Fermi Surface of (CuO₂)_n planes, we exhibit ad-wave solution as well as a generalizeds-wave one.     

Hole Doping and Inhomogeneous Charge Distribution in High Tc Cuprates Investigated from First Principles

To understand the link between doping and electronic properties in the high-temperature superconductors, we have performed first-principles calculations for several representatives of high T _c compounds. In the single-layer cuprate HgBa₂CuO₄ the excess oxygen attracts electrons from the CuO₂ plane leading to an increase of the hole concentration in this building block, where the maximum amount of holes is reached when the dopant oxygen shell is closed. The usage of supercells allows to study the inhomogeneous charge distribution as a function of doping, i.e. from the underdoped up to the overdoped regime. Comparison is made with other compounds like Ba-doped La₂CuO₄ and oxygen-deficient YBa₂Cu₃O_7–x . The effects of our findings on superconductivity are discussed.     

Effect of Oxygen-Deficiency of CuO2 Plane on the Structure, Magnetism, and Transport Properties

Polycrystalline samples La_{2 – x} Sr _x CuO_{4 –} (0.06 x 1.0) and the corresponding vacuum annealed samples were investigated systematically by means of XRD, infrared (IR) spectra, ESR, and resistivity. It is found that the doping of Sr and the oxygen vacancies in CuO₂ planes show different effects on the lattice parameters a and c, and the changes of a and c of La_{2 – x} Sr _x CuO_{4 –} samples (x 0.2) rest with the cooperation of the two factors. The two high frequency IR vibration modes at 500 and 689 cm^–1, which are referred to the vibrations of apical oxygen and planar oxygen, are analyzed in detail. The disappearance of the mode at 689 cm^–1 is interpreted in terms of the screened effect of charge carriers in CuO₂ planes. ESR results indicate that oxygen deficiency of CuO₂ layers not only decreases carrier concentration, but also destroys the antiferromagnetic spin correlation or spin fluctuation and results in localized Cu²⁺ spins. The effect of localized Cu²⁺ spins (or spin scattering) on the superconductivity and transport properties is discussed in the text.     

Composition dependence of transition temperature in new superconductors: La2 −x (Ba,Sr) x CuO4

We have investigated the variation of transition-temperature and coupling parameter with the composition concentration in La_{2 −x} (Ba, Sr) _x CuO₄ superconductors using a formulation developed on the basis of an idea of pairing of charge carriers by exchange of both acoustic plasmons and phonons. Reasonably good agreement is found between the recent experimental results and our theoretical results on the superconducting transition temperature.     

Evidence for a Local Structural Change in La2CuO4.1 Across the Superconducting Transition

Polarized Cu—K edge XAFS (X-ray absorption fine structure) on La₂CuO_4.1 indicate that the radial distribution function of the copper in plane oxygen pairs is a two-site distribution, in agreement with the results found by Bianconi et al. for temperatures below the appearance of a pseudogap. Additionally we find evidence of a change in this distribution across the superconducting transition, suggesting coupling between the local lattice structure and the charged particles involved in the superconductivity.     

A Link between Spin Fluctuation and Fermi Surface in the High T c Cuprates — A Description within the Single-band Hubbard Model

A link between the spin structure and the shape of the Fermi surface is sys-tematically explored for the single-band repulsive Hubbard model with the fluctuation exchange (FLEX) approximation. We show that (i) the ex-perimentally observed band filling dependence of the peak position of the spin structure in the high T _C cuprates can be understood for both the hole-doped (YBCO, Bi2212) and electron-doped (NCCO) regimes. (ii) For La _2?xSr_xCuO₄, the spin-structure incommensurability and the ARPES re-sult for the Fermi surface can be understood simultaneously if the second nearest neighbor hopping decreases with the hole doping.     

Optical Properties of Doped Antiferromagnets

We investigate the consequences of an incommensurate magnetic order in doped La_2–x Sr _x CuO₄ using dynamical mean-field theory for the effective single-band model. The high-energy optical transitions are due to high-energy excitations across large Mott–Hubbard gap, while low-energy excitations involve a pseudogap induced by the local spin order. The latter lead to a strong drop in the scattering rate at low , in qualitative agreement with the experimental data.     

Oxygen deficiency dependence of transition temperature in (Sm, Er) Ba2Cu3O7−δ superconductors

We have investigated the effects of oxygen deficiency (δ) on the transition temperature (T _c) of (Sm, Er)Ba₂Cu₃O₇₋ δ superconductors by incorporating the effects of the two dimensional (2D) acoustic phonons and plasmons in the framework of strong coupling theory. The proposed approach for yttrium cuprates properly takes care of the double CuO₂ plane in a unit cell and has been found earlier to be successful in describing the pairing mechanism as well as the variation ofT _c withδ in Y Ba₂Cu₃O₇₋ δ system. The coupling strength (λ), the screening parameter (μ*) and the two dimensional acoustic phonon (plasmon) energyħω ₋(ω₊) as a function of oxygen deficiency is worked out. Finally, the transition temperature is evaluated and is found to be consistent with the earlier experimental data on yttrium cuprates. Thus, coupled phonon-plasmon mechanism is adequate to understand the nature of pairing mechanism and oxygen deficiency dependence of transition temperature in 90 K (Sm, Er)Ba₂Cu₃O₇₋ δ superconductors.