d-Symmetry superconductivity as a consequence of valence-bond type correlations

It is shown that d _x ²−y ² symmetry of superconducting order due to valence bond (VB) type correlations is possible. The VB correlations are compatible with antiferromagnetic (AF) spin order. For the two-dimensional Hubbard model with arbitrary doping, the variational method of local unitary transformations is used to construct explicitly a uniform state with VB structure. The d-channel attraction of holes is a consequence of the modulation of hops by the populations of centers accompanying VB formation, and the parameters of the modulation are determined variationally. The increase in the density of states at the Fermi level accompanying AF splitting of the band, which is absent in the paramagnetic state, is important for the gap width. The gap width and its ratio to T _c are of the order of 2Δ≃0.1t and 2Δ/kT _c≃4–4.5 with U/t≃8. The agreement between the phase diagram found and experiment is discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 350–355 (10 March 1998)     

Effect of interlayer single-particle hoppings on the superconducting transition temperature

It is well known that the superconducting transition temperature of high-T _c cuprates depends on the number of CuO₂ planes in the unit cell. The multilayer structure implies the possibility of interlayer hopping. Under the assumption that the interlayer hopping can be specified by the parameter t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))², the quasiparticle excitation spectrum for the bilayer cuprate in the superconducting state has been determined in the framework of the t − t′ − t″ − t _⊥ − J* model using the generalized mean-field approximation. It turns out that the interlayer hoppings does not create any additional mechanism of the Cooper paring and does not lead to an increase in T _c . The splitting of the upper Hubbard quasiparticle band attributed to the interlayer hoppings is manifested as two peaks in the doping dependence of the superconducting transition temperature at temperatures below the maximum T _c value for a single-layer cuprate. It has been found that antiferromagnetic interlayer correlations suppress the interlayer splitting. This probably leads to the common doping dependence of T _c for both single-layer and bilayer cuprates.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Physical manifestations of valence-bond structures in correlated systems

Using the Hubbard model and the corresponding t-J model, we study the properties of correlated states with valence-bond structures. Mixed states with such structures and with antiferromagnetic spin ordering can be constructed by means of local unitary transformations of uncorrelated states. The latter turn out to have lower energy than mean-field antiferromagnetic solutions. Spin correlations for various degrees of doping δ=n−1 are in good agreement with the results of exact calculations for finite systems. In contrast to mean-field solutions, allowance for valence-bond correlations leads to a reasonable value of the critical δ, at which long-range antiferromagnetic order disappears. A calculation of the spectral functions that describe photoemission reveals typical behavior in two bands of effective hole (and electron) excitations, and energy transport in bands as the quasimomentum varies from (0,0) to (π,π), consistent with calculations in finite systems. We construct a homogeneous correlated state of fluctuating valence bonds (the band-model analog of states of fluctuating valence bonds), and demonstrate that its energy is lower than that of valence-bond alternant structures. Zh. éksp. Teor. Fiz. 112, 1409–1429 (October 1997)     

Lifshits quantum phase transitions and rearrangement of the Fermi surface upon a change in the hole concentration in high-temperature superconductors

Changes in the electronic structure in the normal phase of high-T _c superconductors (HTSCs), viz., layered cuprates, are considered. The results of LDA + GTB calculations of the electron structure and the Fermi surface of La_{2 − x} Sr _x CuO₄ one-layer cuprates with allowance for strong correlations are compared with ARPES and quantum oscillations data. Two critical points x _c1 and x _c2 are discovered at which the rear-rangement of the Fermi surface takes place. In the vicinity of these points, changes in the thermodynamic properties at low temperatures are determined using the Lifshits ideology concerning 2.5-order quantum phase transitions. A singularity δ(C/T) ∝ (x − x _e )^1/2 in the electron heat capacity agrees well with the available experimental data in the vicinity of x _c1 ≈ 0.15. Sign reversal of the Hall constant upon doping is also considered qualitatively.     

Two-dimensional quantum interference contributions to the magnetoresistance of Nd2−x CexCuO4−δ single crystals

Two-dimensional (2D) weak localization effects at low temperatures T=0.2–4.2 K are investigated in a nonsuperconducting sample Nd_1.88Ce_0.12CuO_4−δ and in the normal state of a superconducting sample Nd_1.82Ce_0.18CuO_4−δ for B>B _c2≃3 T. The phase coherence time τφ (≃5×10⁻¹¹ s at 1.9 K) and the effective thickness d of a conducting CuO₂ layer (≃1.5 Å) are estimated by fitting the expressions from the 2D weak localization theory to the magnetoresistivity data for the normal-to-plane and in-plane magnetic fields. The estimated value of the parameter d ensures the condition of strong carrier confinement and justifies a model of almost decoupled 2D metallic sheets for the Nd_2−x Ce_xCuO_4−δ single crystals. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 93–99 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Doping-dependent electronic structure of cuprates studied using angle-scanned photoemission

Full k -maps of the electronic structure near the Fermi level of differently doped cuprates measured with angle-scanned photoelectron spectroscopy are presented. The valence band maximum of the antiferromagnetic insulator Sr₂CuO₂Cl₂, which is taken as a representative of an undoped cuprate, and the Fermi surfaces of overdoped, optimally doped and underdoped Bi₂Sr₂CaCu₂O_8+δ high-temperature superconductors are mapped in the normal state. The results confirm the existence of large Luttinger Fermi surfaces at high doping with a Fermi surface volume proportional to (1+x), where x is the hole concentration. At very low doping, however, we find that this assumption based on Luttinger's theorem is not fulfilled. This implies a change in the topology of the Fermi surface. Furthermore the intensity of the shadow bands observed on the Fermi surface of Bi₂Sr₂CaCu₂O_8+δ as a function of the doping is discussed. Received 12 October 1999 and Received in final form 12 April 2000     

Probing the field-induced variation of the chemical potential in Bi2Sr2CaCu2Oy via magneto-thermopower measurements

Approximating the shape of the magneto-thermoelectric power (TEP) ΔS(T,H) measured in Bi₂Sr₂CaCu₂O_y by an asymmetric linear triangle of the form ΔS(T,H)≃S _p (H)±B ^±(H)(T _c −T) with positive B ⁻(H) and B ⁺(H) defined below and above T _c , we observe that B ⁺(H) ≃2B ⁻(H). To account for this asymmetry, we explicitly introduce the field-dependent chemical potential μ(H) of holes into the Ginzburg-Landau theory and calculate both an average ΔS _av(T,H) and fluctuation contribution ΔS _fl(T,H) to the total magneto-TEP ΔS(T,H). As a result, we find a rather simple relationship between the field-induced variation of the chemical potential in this material and the above-mentioned magneto-TEP data around T _c , viz. Δ μ(H)∝S _p (H). Zh. éksp. Teor. Fiz. 116, 257–262 (July 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Electronic plus phonon-exchange mechanism for high-temperature superconductivity in layered crystals

A general mathematical formulation is developed for calculating the effective electron-electron interaction in layered crystals like YBa₂Cu₃O_7−δ, and for finding the resulting superconducting transition temperatureT _c in such systems within the framework of the conventional BCS pairing arising from various possible excitations in the medium. This differs considerably from the usual case of an effective three-dimensional homogeneous system, and should be relevant in the calculation ofT _c for the new class of high-T _c perovskites in which oxygen deficiencies in Cu-O layers and their distribution in the crystal play a crucial role. The explicit form of the effective interactionV _jj(q _t,ω) in a given layerj in the unit cell of the crystal is found to be determined not only by the true polarization functionπ _j(q _t,ω) of that layer, but also of other layers. The exchange of electronic excitations of a nearby insulating layer by carriers in a conducting layer thus becomes possible to get highT _c, with or without the usual phonon exchange.     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Spin susceptibilities for the Hubbard model in a band approach

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω(Q)=c|Q−(π, π)| near Q∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X″(Q,ω→0) gives the same mode with a peak at Q∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X″(Q,ω→0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector. Zh. éksp. Teor. Fiz. 116, 1058–1080 (September 1999)     

Anomalous temperature behavior of the resistivity in lightly doped manganites around a metal-insulator phase transition

An unusual temperature and concentration behavior of the resistivity ρ(T, x) in La_0.7Ca_0.3Mn_1−2x Cu_xO₃ is observed at slight Cu doping (0≤x≤0.05). Namely, the introduction of copper results in a splitting of the resistivity maximum around the metal-insulator transition temperature T ₀(x) into two differently evolving peaks. Unlike the original Cu-free maximum, which steadily increases with doping, the second (satellite) peak remains virtually unchanged for x<x _c , increases for x≥x _c , and finally disappears at x _m ≃2x _c , with x _c ≃ 0.03. The observed phenomenon is thought to arise from a competition between substitution-induced strengthening of the potential barriers (which hinder the charge hopping between neighboring Mn sites) and weakening of the kinetic energy of the carriers. The data are well fitted by assuming a nonthermal tunneling conductivity theory with randomly distributed hopping sites. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 473–478 (10 October 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Dependence of the critical temperature of high-temperature cuprate superconductors on hoppings and spin correlations between CuO<Subscript>2</Subscript> planes

The influence of interlayer hoppings on the superconducting transition temperature (T _c) in bilayer cuprates has been studied. The parameter of hopping between layers is expressed as t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))² and treated as a small perturbation for the states of two CuO₂ planes described by the t-t′-t″-J* model. In the generalized mean field approximation for d_{x² - y²}{d_{{x^2} - {y^2}}} symmetry of the superconducting gap, neither the interlayer hopping or exchange interaction, nor the pair hopping between CuO₂ layers provides an additional mechanism of Cooper pair formation or an increase in T _c. In the concentration dependence of T _c, the bilayer splitting of the upper Hubbard band of quasi-holes is manifested as two peaks with temperatures slightly lower than the maximum T _c for a single-layer cuprate. Interlayer antiferromagnetic spin correlations suppress bilayer splitting.     

Effect of γ irradiation on the hysteresis phenomena at the incommensurate-commensurate phase transition in Rb2ZnBr4

The effect of γ irradiation on the temperature hysteresis in dielectric permittivity ɛ and loss tangent tan δ of crystalline Rb₂ZnBr₄ has been studied in the vicinity of the incommensurate-commensurate phase transition. The ɛ(T) and tan δ(T) curves were found to exhibit anomalies in the form of maxima. Hysteresis was observed in the measured properties, including the transition temperature T _c (ΔT=T _c ^h −T _c ^c ), in both unirradiated and irradiated samples. It is shown that, as the radiation dose increases the extent of the hysteresis ΔT increases, the values of ɛ _max and tan δ _max at the transition point decrease, and the anomalies wash out. Fiz. Tverd. Tela (St. Petersburg) 40, 1911–1914 (October 1998)     

Measurement of the spindependent relative conversion coefficients in α-Fe and α-Fe2O3

The relative differences δ _ns (n=1, 2, 3) of the spindependent conversion coefficients were measured for α-Fe and α=Fe₂O₃. In contrast to theoretical predictions of δ_1s≃−10⁻⁵ we found δ_1s≃−1.0(4)x10⁻² for both α-Fe and α-Fe₂O₃. As a possible source for this difference we consider a dynamic coupling with the atomic spin during the conversion process.     

Calculation of the Fermi surface with complex topology from norm-conserving cluster perturbation theory for doping dependent electronic structure of the Hubbard model

The results of recently developed norm-conserving cluster perturbation theory for doping dependent electronic structure of the Hubbard model are reported. We have found that the momentum distribution of the spectral weight strongly depends on the broadening value δ. At δ = 0.1t, we reproduce the angle-resolved photoemission spectroscopy data, while at δ = 0.01t we obtain two quantum phase transitions.     

Advances in single crystal growth and annealing treatment of electron-doped HTSC

High quality electron-doped HTSC single crystals of Pr_2−xCe_xCuO_4+δ and Nd_2−xCe_xCuO_4+δ have been successfully grown by the container-free traveling solvent floating zone technique. The optimally doped Pr_2−xCe_xCuO_4+δ and Nd_2−xCe_xCuO_4+δ crystals have transition temperatures T _c of 25 K and 23.5 K, respectively, with a transition width of less than 1 K. We found a strong dependence of the optimal growth parameters on the Ce content x. We discuss the optimization of the post-growth annealing treatment of the samples, the doping extension of the superconducting dome for both compounds as well as the role of excess oxygen. The absolute oxygen content of the as-grown crystals is determined from thermogravimetric experiments and is found to be ≥ 4.0. This oxygen surplus is nearly completely removed by a post-growth annealing treatment. The reduction process is reversible as demonstrated by magnetization measurements. In as-grown samples the excess oxygen resides on the apical site O(3). This apical oxygen has nearly no doping effect, but rather influences the evolution of superconductivity by inducing additional disorder in the CuO₂ layers. The very high crystal quality of Nd_2−xCe_xCuO_4+δ is particularly manifest in magnetic quantum oscillations observed on several samples at different doping levels. They provide a unique opportunity of studying the Fermi surface and its dependence on the carrier concentration in the bulk of the crystals.     

Pairing type change upon an increase in the cerium doping level in the Nd<Subscript>2 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>CuO<Subscript>4 + δ</Subscript> electronic superconductor

We report on the results of analyzing the temperature dependences of the resistivity of the Nd_{2 − x} Ce _x CuO_{4 + δ} electronic superconductor with x = 0.14 (underdoped range), x = 0.15 (optimal doping), and x = 0.18 (overdoped range) and with various degrees of annealing in an oxygen-free atmosphere in magnetic fields up to H = 90 kOe (H ‖ c, J ‖ ab) in the temperature range T = (0.4–300) K. It is shown that the observed differences in the dependences of the slope of the upper critical field (dH_c2 /dT)|_Tc (dH_{c2} /dT)|_{T_c } on the degree of disorder in the Nd_{2 − x} Ce _x CuO_{4 + δ} system upon a change in the cerium doping level indicate a change in the symmetry of d-type pairing to anisotropic s pairing.     

Possible manifestation of spin fluctuations in the temperature behavior of the resistivity of Sm<Subscript>1.85</Subscript>Ce<Subscript>0.15</Subscript>CuO<Subscript>4</Subscript> thin films

A pronounced step-like (kink) behavior in the temperature dependence of resistivity ρ(T) is observed in the optimally doped Sm_1.85Ce_0.15CuO₄ thin films around T _sf = 87 K and attributed to the manifestation of strong-spin fluctuations induced by Sm³⁺ moments with the energy ħω_sf = k _B T _sf ≃ 7 meV. The experimental data are found to be well fitted by the residual (zero-temperature) ρ_res, electron-phonon ρ_e-ph(T) = AT, and electron-electron ρ_e-e(T) = BT ² contributions in addition to the fluctuation-induced contribution ρ_sf(T) due to thermal broadening effects (of the width ω_sf). According to the best fit, the plasmon frequency, impurity scattering rate, electron-phonon coupling constant, and Fermi energy are estimated as ω_p = 2.1 meV, τ ₀ ⁻¹ = 9.5 × 10⁻¹⁴ s⁻¹, λ = 1.2, and E _F = 0.2 eV, respectively. The text was submitted by the authors in English.     

Pseudovector heavy quarkonia in e + e −2 collisions

It is shown that BR(χ _b1(1 P)→e ⁺ e ⁻)≃3.3· 10⁻⁷ and BR(χ _c1(1 P)→e ⁺ e ⁻)≃10⁻⁸. This gives realistic possibilities for searching for the production of χ _b1(1 P) and ξ _c1(1 P) states in e ⁺ e ⁻ collisions, even on the present-day colliders, to say nothing of b and c-τ factories. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 569–574 (25 April 1996)