Cuprate Planes Research Articles

Zhang-Rice singlets dominate critical temperature evolution of cuprate superconductivity

We show that formation of Zhang-Rice singlets (ZRS) naturally explains the empirical superconducting dome by random distribution of holes in copper-oxygen plane of cuprates. A general relation Tc/Tcmax=25(c-0.04), where c is the concentration of the ZRS and Tcmax is the maximum of critical temperature Tc, is obtained and reproduces the doping-dependent critical temperature evolution in the whole superconducting dome. The relation has been applied to estimate the effects of impurities substituting copper in the copper-oxygen plane. Our relation successfully predicts the suppression of superconductivity due to the substitution of Cu by the impurities. We demonstrate that Tc decreases linearly with the increase of the impurity concentration and the scattering range plays a key role in the suppression of the superconductivity. These results agree well with the experimental observations of the substitutions by Zinc and Nickel. Our relation is universal for all families of cuprates and explains the formation of the superconducting dome in the phase diagram.

Компьютерное моделирование наноскопических фазово-неоднородных состояний и фазовых диаграмм ВТСП купратов и никелатов

More than 35 years of experience in the study of cuprate superconductors shows that the main characteristics of the phase diagram can only be obtained by taking into account mesoscopic static/dynamic phase inhomogeneity as a key property of these materials. Within a minimal model for the CuO2 planes with the on-site Hilbert space reduced to only three effective valence centers [CuO4]7-,6-,5- (nominally Cu1+,2+,3+) with different conventional spin and different orbital symmetry we propose a unified non-BCS model that allows one to describe the main features of the phase diagrams of doped cuprates within the framework of a simple effective field theory. Using Maxwell's construction, the global nature of the electronic phase separation in the CuO2 planes of HTSC cuprates is established, which makes it possible to understand and explain many fundamental features of the physics of the normal and superconducting state of cuprates, including the mechanism of formation of the HTSC and pseudogap phase. The features of phase-inhomogeneous states and their evolution with temperature and doping degree, including the special role of the impurity potential in cuprates/nickelates with nonisovalent substitution, are considered for particular examples of the charge triplet model in the framework of the classical Monte Carlo method.

Pseudogap state and unusual metallic conductivity in high-Tc cuprate superconductors

The BCS-like pairing of polaronic carriers in underdoped and optimally doped high-Tc cuprates above the superconducting transition temperature Tc is considered. Such a BCS-like pairing correlation leads to the formation of bosonic Cooper pairs and the appearance of a pseudogap on the Fermi surface at a characteristic temperature T* > Tc. It is shown that the calculated doping dependence of the BCS-like pseudogap agrees quite well with the experimentally observed doping dependence of the pseudogap in La2–xSrxCuO4 (where x is the doping level). The mechanisms of the unusual metallic transports of different types of charge carriers above and below T* along the CuO2 layers (i.e., ab planes) in high-Tc cuprates are identified. The conductivity of the three types of charge carriers (large polarons, excited Fermi components of bosonic Cooper pairs, and bosonic Cooper pairs themselves) at their scattering by lattice vibrations is considered. It is established that the linear temperature dependence of the in-plane resistivity ρab (T) observed, as a rule, in underdoped and optimally doped cuprates above T* is associated with the scattering of polaronic carriers by acoustic and optical phonons. Theoretical results compared with the experimental data allow for confirming that the different (upward and downward) deviations from the linearity in ρab (T) below T* and the most interesting resistive transitions [i.e., a clear jump and a sharp drop in ρab (T)] at T = T* are caused by the pseudogap effect on the conductivity of the excited Fermi components of bosonic Cooper pairs and by the excessive conductivity of bosonic Cooper pairs in high-Tc cuprates above Tc.

Computer simulation of nanoscopic phase-inhomogeneous states and phase diagrams of HTSC cuprates and nickelates

More than 35 years of experience in the study of cuprate superconductors shows that the main characteristics of the phase diagram can only be obtained by taking into account mesoscopic static/dynamic phase inhomogeneity as a key property of these materials. Within a minimal model for the CuO2/NiO2 planes with the on-site Hilbert space reduced to only three effective valence centers [CuO4]7-,6-,5- (nominally Cu1+,2+,3+) with different conventional spin and different orbital symmetry we propose a unified non-BCS model that allows one to describe the main features of the phase diagrams of doped cuprates within the framework of a simple effective field theory. Using Maxwell's construction, the global nature of the electronic phase separation in the CuO2 planes of HTSC cuprates is established, which makes it possible to understand and explain many fundamental features of the physics of the normal and superconducting state of cuprates, including the mechanism of formation of the HTSC and pseudogap phase. The features of phase-inhomogeneous states and their evolution with temperature and doping degree, including the special role of the impurity potential in cuprates/nickelates with nonisovalent substitution, are considered for particular examples of the charge triplet model in the framework of the classical Monte Carlo method. Keywords: cuprates, nickelates, effective field theory, phase diagram, phase separation, Monte-Carlo.

Charge-stripe order, antiferromagnetism, and spin dynamics in the cuprate-analog nickelate La4Ni3O8

We report a muon spin rotation ($\mu$SR) study of the cuprate-analog nickelate La$_4$Ni$_3$O$_8$, which undergoes a transition at 105 K to a low-temperature phase with charge-stripe and antiferromagnetic (AFM) order on square planar NiO$_2$ layers. Zero-field $\mu$SR shows that this transition is abrupt and that the AFM configuration is commensurate. Comparison of observed muon precession frequencies with Ni dipolar field calculations yields Ni moments $\lesssim 0.5\mu_B$. Dynamic muon spin relaxation above 105 K suggests critical slowing of Ni spin fluctuations, but is inconsistent with corresponding $^{139}$La NMR results. Critical slowing and an abrupt transition are also observed in the planar cuprate AFM La$_2$CuO$_{4+\delta}$, where they are evidence for weakly interplanar-coupled two-dimensional AFM spin fluctuations, but our $\mu$SR data do not agree quantitatively with theoretical predictions for this scenario.

Magnetic orders in the hole-doped three-band Hubbard model: Spin spirals, nematicity, and ferromagnetic domain walls

The Copper-Oxygen planes in cuprates have been at the center of the search for a theory of high-temperature superconductivity. We conduct an extensive study of the ground state of the three-band Hubbard (Emery) model in the underdoped regime. We focus on the magnetic and charge orders, and present results from generalized Hartree-Fock (GHF) calculations. The ground-state properties at the thermodynamic limit are challenging to pin down because of sensitivity to computational details including the shapes and sizes of the supercells. We employ large-scale computations with various technical improvements to determine the orders within GHF. The ground state exhibits a rich phase diagram with hole doping as the charge transfer energy is varied, including ferromagnetic domain walls embedded in an antiferromagnetic background, spin spirals, and nematic order.

Instability towards staggered loop currents in the three-orbital model for cuprate superconductors

We present evidence for the existence of a spontaneous instability towards an orbital loop-current phase in a multiorbital Hubbard model for the CuO$_2$ planes in cuprates. Contrary to the previously proposed $\theta_{II}$ phase with intra-unit cell currents, the identified instability is towards a staggered pattern of intertwined current loops. The orbitally resolved current pattern thereby shares its staggered character with the proposal of d-density wave order. The current pattern will cause a Fermi surface reconstruction and the opening of a pseudogap. We argue that the pseudogap phase with time-reversal symmetry breaking currents is susceptible to further phase transitions and therefore offers a route to account for axial incommensurate charge order and a polar Kerr effect in underdoped cuprates.

Critical Behavior of Dynamical Chiral Symmetry Breaking with Gauge Boson Mass in QED3**Supported by the Natural Science Foundation of Jiangsu Province under Grant No BK20130387, and the Fundamental Research Funds for the Central Universities under Grant No 2242014R30011.

Since the massless quantum electrodynamics in 2+1 dimensions (QED3) with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζc. Based on the feature of chiral susceptibility, we show that the system at ζc exhibits a second-order phase transition which accords with the nature of appearance of the high-Tc superconductivity, and the estimated critical exponents around ζc are illustrated.

Quantum and thermal ionic motion, oxygen isotope effect, and superexchange distribution inLa2CuO4

We study the zero-point and thermal ionic motion in La$_2$CuO$_4$ by means of high-resolution neutron diffraction experiments. Our results demonstrate anisotropic motion of O and to a lesser extent of Cu ions, both consistent with the structure of coupled CuO$_6$ octahedra, and quantify the relative effects of zero-point and thermal contributions to ionic motion. By substitution of $^{18}$O, we find that the oxygen isotope effect on the lattice dimensions is small and negative ($-0.01\%$), while the isotope effect on the ionic displacement parameters is significant ($-6$ to $50\%$). We use our results as input for theoretical estimates of the distribution of magnetic interaction parameters, $J$, in an effective one-band model for the cuprate plane. We find that ionic motion causes only small ($1\%$) effects on the average value $\langle J\rangle$, which vary with temperature and O isotope, but results in dramatic ($10$-$20\%$) fluctuations in $J$ values that are subject to significant ($8$-$12\%$) isotope effects. We demonstrate that this motional broadening of $J$ can have substantial effects on certain electronic and magnetic properties in cuprates.

Charge Inhomogeneity in Electron-Doped Pr1.85Ce0.15CuO4 Determined with 63Cu NMR

Nuclear Magnetic Resonance (NMR) of Cu and O has been applied successfully to probe locally the charge distribution in the CuO2 plane of the hole-doped cuprates. However, for the electron-doped systems, only insufficient Cu NMR data are available. Here, with a set of new 63Cu NMR experiments including double-resonance experiments, we examine the quadrupole interaction for a single crystal of Pr1.85Ce0.15CuO4. From the data, we deduce that the doped electrons mainly enter the Cu \(3\mathrm{d}_{x^{2}-y^{2}}\) orbital resulting in an almost vanishing electric field gradient. In addition, we observe a substantial variation across the CuO2 plane that, however, remains largely axially symmetric. We estimate 13 % doped carriers at 15 % nominal doping with a charge density variation of at least 4 % for this optimally doped sample.

Different doping from apical and planar oxygen vacancies in Ba2CuO4−δand La2CuO4−δ: First-principles band structure calculations

First-principles band structure calculations for large supercells of Ba${}_{2}$CuO${}_{4\ensuremath{-}\ensuremath{\delta}}$ and La${}_{2}$CuO${}_{4\ensuremath{-}\ensuremath{\delta}}$ with different distributions and concentrations of oxygen vacancies show that the effective doping on copper sites strongly depends on where the vacancy is located. A vacancy within the Cu layer produces a weak doping effect while a vacancy located at an apical oxygen site acts as a stronger electron dopant on the copper layers and gradually brings the electronic structure close to that of La${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$. These effects are robust and only depend marginally on lattice distortions. Our results show that deoxygenation can reduce the effect of traditional La/Sr or La/Nd substitutions. Our study clearly identifies location of the dopant in the crystal structure as an important factor in doping of the cuprate planes.

Charge compensation and optimal stoichiometry in superconducting (CaxLa1−x)(Ba1.75−xLa0.25+x)Cu3Oy

The superconductive and magnetic properties of charge-compensated (Ca${}_{x}$La${}_{1\ensuremath{-}x}$)(Ba${}_{1.75\ensuremath{-}x}$La${}_{0.25+x}$)Cu${}_{3}$O${}_{y}$ (normally denoted as CLBLCO) are considered through quantitative examination of data for electrical resistivity, magnetic susceptibility, transition width, muon-spin rotation, x-ray absorption, and crystal structure. A derivative of LaBa${}_{2}$Cu${}_{3}$O${}_{y}$, cation doping of this unique tetragonal cuprate is constrained by compensating La substitution for Ba with Ca substitution for La, where for 0 \ensuremath{\le} $x$ \ensuremath{\le} 0.5 local maxima in ${T}_{C}$ occur for $y$ near 7.15. It is shown that optimum superconductivity occurs for 0.4 \ensuremath{\le} $x$ \ensuremath{\le} 0.5, that the superconductivity and magnetism observed are nonsymbiotic phenomena, and that charge-compensated doping leaves the carrier density in the cuprate planes nearly invariant with $x$, implying that only a small fraction of superconducting condensate resides therein. Applying a model of electronic interactions between physically separated charges in adjacent layers, the mean in-plane spacing between interacting charges, $\ensuremath{\ell}=7.1206$ \AA{}, and the distance between interacting layers, \ensuremath{\zeta} = 2.1297 \AA{}, are determined for $x$ = 0.45. The theoretical optimal ${T}_{C0}\ensuremath{\propto}{\ensuremath{\ell}}^{\ensuremath{-}1}{\ensuremath{\zeta}}^{\ensuremath{-}1}$ of 82.3 K is in excellent agreement with experiment (\ensuremath{\approx}80.5 K), bringing the number of compounds for which ${T}_{C}$${}_{0}$ is accurately predicted to 37 from six different superconductor families (overall accuracy of $\ifmmode\pm\else\textpm\fi{}$1.35 K).

Gauge approach to the ‘pseudogap’ phenomenology of the spectral weight in high Tc cuprates

We assume the t–t′–J model to describe the CuO2 planes of hole-doped cuprates and we adapt the spin–charge gauge approach, previously developed for the t–J model, to describe the holes in terms of a spinless fermion carrying the charge (holon) and a neutral boson carrying spin 1/2 (spinon), coupled by a slave-particle gauge field. In this framework we consider the effects of a finite density of incoherent holon pairs in the normal state. Below a crossover temperature, identified as the experimental ‘upper pseudogap’, the scattering of the ‘quanta’ of the phase of the holon-pair field against holons reproduces the phenomenology of nodal Fermi arcs coexisting with a gap in the antinodal region. We thus obtain a microscopic derivation of the main features of the hole spectra due to the pseudogap. This result is obtained through a holon Green function which follows naturally from the formalism and analytically interpolates between a Fermi liquid-like and a d-wave superconductor behaviour as the coherence length of the holon-pair order parameter increases. By inserting the gauge coupling with the spinon we construct explicitly the hole Green function and calculate its spectral weight and the corresponding density of states. So we prove that the formation of holon pairs induces a depletion of states on the hole Fermi surface. We compare our results with ARPES and tunnelling experimental data. In our approach the hole preserves a finite Fermi surface until the superconducting transition, where it reduces to four nodes. Therefore we propose that the gap seen in the normal phase of cuprates is due to the thermal broadening of the SC-like peaks masking the Fermi-liquid peak in the spectral weight. The Fermi arcs then correspond to the region of the Fermi surface where the Fermi-liquid peak is unmasked.

Identification of the muon stopping sites in GdSr2Cu2RuO8: Confirmation of ferromagnetic cuprate planes in a superconducting cuprate

Muon spin rotation experiments on superconducting GdSr2Cu2RuO8 reported a magnetic induction of 720–740G. Neutron diffraction studies have shown that the Ru spins are ordered antiferromagnetically along the c-axis, while the cuprate planes are ordered ferromagnetically in the a–b plane and are stacked antiferromagnetically. Using this spin configuration with refined spin moments, we have calculated the magnetic induction at potential muon stopping sites; muons stopping in the center of the ferromagnetic CuO2 planes will experience an induction of ∼725G, a result in excellent agreement with experiment. We predict that muon experiments, carried out at temperatures below the Gd antiferromagnetic ordering temperature, will detect an induction exceeding 1T at one of the muon sites.

Frustrated quantum two-dimensional J 1-J 2-J 3 antiferromagnet in a spherically symmetric self-consistent approach

In the framework of a spherically symmetric self-consistent approach to two-time retarded spin-spin Green’s functions, we develop the theory of a two-dimensional frustrated J1-J2-J3 quantum S=1/2 antiferromagnet. We show that taking the damping of spin fluctuations into account is decisive in forming both the spin-liquid state and the state with long-range order. In particular, the existence of damping allows explaining the scaling behavior of the susceptibility χ(q, ω) of the CuO2 cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable χ(q, ω) peak. In the case of the complete J1-J2-J3 model, in a single analytic approach, we find continuous transitions between three phases with long-range order (“checkerboard,” stripe, and helical (q, q) phases) through the spin-liquid state. We obtain good agreement with cluster computations for the J1-J2-J3 model and agreement with the neutron scattering data for the J1-J2 model of cuprates.

True charge-transfer gap in parent insulating cuprates

A large body of experimental data point towards a charge transfer instability of parent insulating cuprates to be their unique property. We argue that the true charge transfer gap in these compounds is as small as 0.4-0.5\,eV rather than 1.5-2.0\,eV as usually derived from the optical gap measurements. In fact we deal with a competition of the conventional (3d$^9$) ground state and a charge transfer (CT) state with formation of electron-hole dimers which evolves under doping to an unconventional bosonic system. Our conjecture does provide an unified standpoint on the main experimental findings for parent cuprates including linear and nonlinear optical, Raman, photoemission, photoabsorption, and transport properties anyhow related with the CT excitations. In addition we suggest a scenario for the evolution of the CuO$_2$ planes in the CT unstable cuprates under a nonisovalent doping.

X-ray absorption near-edge spectra of overdopedLa2−xSrxCuO4high-Tcsuperconductors

We present results for realistic modeling of the x-ray absorption near edge structure (XANES) of the overdoped high-T_c superconductor La_2-xSr_xCuO_4 in the hole doping range x = 0.20-0.30. Our computations are based on a real-space Green's function approach in which strong-correlation effects are taken into account in terms of a doping-dependent self-energy. The predicted O K-edge XANES is found to be in good accord with the corresponding experimental results in this overdoped regime. We find that the low energy spectra are dominated by the contribution of O-atoms in the cuprate planes, with little contribution from apical O-atoms.

Electronic structure of hole centers in CuO2 planes of cuprates

A theoretical analysis and a large amount of experimental data indicate that the structure of the valence hole states in doped cuprates is more complicated than assumed in the simple Zhang-Rice singlet model. In fact, we are dealing with a competition between a hybrid Cu3d–O2pb1g∝dx2−y2-state and purely oxygen nonbonding states with a2g- and eux,y∝px,y-symmetries. Thus, as a cluster analog of a Cu3+ ion, the ground state of a non-Zhang-Rice CuO45− hole center of this sort should be described by complicated A1g1−B2g1,3−Eu1,3 multiplet with a set of charge, orbital, and spin order parameters, some of which are well known (e.g., spin moment or “ferromagnetic” Ising orbital momentum localized on oxygen ions) while others are unconventional or hidden (e.g., “antiferromagnetic” ordering of Ising orbital momenta localized on four oxygen atoms or a combined spin-orbital-quadrupole ordering). The non-Zhang-Rice CuO45− centers are actually singlet-triplet pseudo-Jahn-Teller centers with strong vibron coupling to the lattice. The complicated structure of the ground-state multiplet of the hole centers shows up in many of the unusual properties of doped cuprates, in particular, their pseudo-gap phase.

Array of Josephson junctions with a nonsinusoidal current-phase relation as a model of the resistive transition of unconventional superconductors

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modeling the transition in high-Tc superconductors. The emergence of higher harmonics, besides the simple sinusoid Ic sin ϕ, is expected for dominant d-wave symmetry of the Cooper pairs, random distribution of potential drops, dirty grains, or nonstationary conditions. We show that additional cosine and sine terms act, respectively, by modulating the global resistance and by changing the Josephson coupling of the mixed superconductive-normal states. First, the approach is applied to simulate the transition in disordered granular superconductors with the weak-links characterized by nonsinusoidal current-phase relation. In granular superconductors, the emergence of higher-order harmonics affects the slope of the transition. Then, arrays of intrinsic Josephson junctions, naturally formed by the CuO2 planes in cuprates, are considered. The critical temperature suppression, observed at values of hole doping close to p=1/8, is investigated. Such suppression, related to the sign change and modulation of the Josephson coupling across the array, is quantified in terms of the intensities of the first and second sinusoids of the current-phase relation. Applications are envisaged for the design and control of quantum devices based on stacks of intrinsic Josephson junctions.

Two-magnon Raman scattering in dielectric and superconducting YBa2Cu3O6+x crystals

Two-magnon Raman scattering in dielectric, as well as superconducting, YBa2Cu3O6 + x single crystals with mobile oxygen content x = 0.2–0.7 and superconducting transition temperature T c = 0–74 K is studied in detail. Doping with oxygen in the range of x = 0.2–0.5 leads to two-magnon scattering peak broadening and a shift in the spectral position of the peak towards lower energies. The most significant qualitative changes in two-magnon scattering in YBa2Cu3O6 + x crystals are observed in a narrow oxygen concentration range near x = 0.7. This is explained by a considerable decrease in the correlation length ξAF of antiferromagnetic (AF) correlations upon an increase in the concentration of free carriers. For instance, doping is accompanied with a reduction of ξAF to values of several lattice constants a for x ≈ 0.7, a transition to the regime of short-range AF order, and local scattering of light from a small AF cluster with a size of 3 × 4 lattice constants. An increase in the free charge carrier concentration destroys the short-range AF order in a narrow range of the stoichiometry index near x = 0.7. Experimental data also indicate heterogeneity of cuprate planes at microscopic level, which leads to coexistence of superconducting and AF regions in YBa2Cu3O6 + x super-conducting crystals.