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.     

Spectral properties of doped bilayer cuprates at finite temperatures

Recently, angle-resolved photoemission spectroscopy measurements on Bi₂Sr₂CaCu₂O_8+δ, which possesses two CuO₂ layers in the same unit cell, have yielded very interesting results. For the overdoped samples, these results show a splitting of electronic states near k=(π, 0) point of Brillioun zone. On the other hand, no splitting is observed in the underdoped samples. In view of this, the detailed studies including the doping and temperature dependence of the spectral properties become desirable. In this paper, we consider cuprates possessing two CuO₂ layers per unit cell. Each layer in the system is described by the t-t ¹-J model and the two layers are coupled via an intrabilayer hopping term (t _⊥) and an intrabilayer exchange coupling (J _⊥). A self-consistent perturbation approach is used to calculate the electronic spectral function for different values of hole density, hole momentum and temperature. We find that the imaginary part of the self energy is strongly momentum dependent which contradicts the suggestion that the Fermi surface of cuprates may be described by marginal Fermi liquid theory. We have calculated the spectral function for various values of intrabilayer parameters t _⊥ and J _⊥. For larger values of intrabilayer interactions we observe the splitting in the quasi-particle peak at k=(π, 0) which is in agreement with the recent observations. The splitting is also found to be sensitive to the hole concentration as well as the temperature of the system. We have also discussed the reasons why the splitting is absent in underdoped bilayer cuprates at low temperature.     

Pseudogap behavior in Bi<Subscript>2</Subscript>Ca<Subscript>2</Subscript>SrCu<Subscript>2</Subscript>O<Subscript>8</Subscript>: Results of the generalized dynamical mean-field approach

Pseudogap phenomena are observed for the normal underdoped phase of different high-T _c cuprates. Among others, the Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σ_k hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σ_k in the spirit of our recently proposed DMFT + Σ_k approach taking into account pseudogap fluctuations. In the present model, Σ_k describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x ² − y ² orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σ_k quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σ_k successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σ_k Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments. The article was submitted by the authors in English.     

Phase diagram for a t-J bilayer: role of interlayer couplings

The phase diagram for a t-J bilayer as a function of interplanar hopping, t_⊥ and hole concentration, x is presented for a few different values of interplanar exchange, J_⊥ using variational Monte Carlo calculations. The phase diagram shows rich features, such as a coexistence of antiferromagnetism and superconductivity at underdoping, planar (d-wave) and interplanar (d_z-wave) superconducting correlations for small and large J_⊥, respectively at optimal and overdoping. Another unusual feature appears in the form of a dome shaped structure in the phase diagram where the superconducting correlations are initially assisted as interplanar hopping is enhanced for small t_⊥, while larger t_⊥ is found to be detrimental to superconductivity.     

Bilayer exchange coupling and neel temperature of YBa2Cu3O6.2

The present paper attempts to study the Neel temperature of bilayer antiferromagnetic cuprate YBa₂Cu₃O_6.2 within anisotropic Heisenberg model. The double time Green’s function formalism within random phase approximation (RPA) has been used to obtain various correlation functions. The magnetization and the Neel temperature (T _N) are evaluated. It is observed that the ratio of intrabilayer to inplane exchange coupling (r=J⊥/J‖) plays an important role in the magnetic dynamics of bilayer systems. The recent experimental data of bilayer system YBa₂Cu₃O_6.2 have been used to estimate the ratio r from the expression for Neel temperature. The estimated values of spin gap and the ratio of hopping matrix elements t⊥/t‖ are found to be in fairly good agreement with the existing experimental results.     

Condensation energy of the superconducting bilayer cuprates

In the present work, we report the interplay of single particle and Cooper pair tunnelings on the superconducting state of layered high-T _c cuprate superconductors. For this we have considered a model Hamiltonian incorporating the intra-planar interactions and the contributions arising due to the coupling between the planes. The interplanar interactions include the single particle tunneling as well as the Josephson tunneling of Cooper pairs between the two layers. The expression of the out-of-plane correlation parameter which describes the hopping of a particle from one layer to another layer in the superconducting state is obtained within a Bardeen-Cooper-Schriefer (BCS) formalism using the Green’s function technique. This correlation is found to be sensitive to the various parameter of the model Hamiltonian. We have calculated the out-of-plane contribution to the superconducting condensation energy. The calculated values of condensation energy are in agreement with those obtained from the specific heat and the c-axis penetration depth measurements on bilayer cuprates.     

Physical quantities for two coupled Hubbard planes and comparison with experiments on Bilayer high-Tc cuprates

For a bilayer model of the high-T_c cuprates consisting of two coupled Hubbard planes we calculate within the FLEX (fluctuation exchange) approximation the quasiparticle self-energies and dynamic spin susceptibilities. We consider a Fermi surface similar to those of the YBaCuO cuprates, an on-site Coulomb repulsion U = 6 t (where t is the intraplane hopping), and interplane hoppings t’ up to t’ = 0.7 t. For sufficiently large t'(?0.3 t) the spin susceptibility gC^? due to transitions between the bonding and antibonding states becomes much larger than the susceptibility gC⁺ for transitions within the same band. The spectral density Im gC^?(q, ω) exhibits a peak centered at the antiferromagnetic wavevector q = Q = (π, π) and at the antiparamagnon frequency ω = ω_sf. For decreasing temperature T and increasing t’ the peak becomes more and more pronounced. We calculate the Fermi lines of the bonding and antibonding bands for different t'. The superconducting transition temperature T_c for d_x ²?y²-wave pairing decreases as t' increases. Our results are in qualitative agreement with magnetic neutron scattering, magnetic resonance, and photoemission experiments on bilayer YBaCuO cuprates. They are also consistent with the results of quantum Monte Carlo simulations.     

d-symmetry superconductivity due to valence bond correlations

It is shown that d-symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d-channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the T _c are 2Δ≃0.1t and 2Δ/kT _c≃4.5−4 for U/t≃8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of T _c on the doping δ=|n−1| and the Fermi surface shape are highly sensitive to the weak interaction t′ leading to diagonal hoppings. In the case of t′>0 and p-doping, the peak on the curve of T _c(δ) occurs at the doping δ _opt, when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k∼(π,0). In underdoped samples with δ<δ _opt, the anisotropic pseudogap in the normal state corresponds to the energy difference |E(π,0)−μ| between this part of the spectrum and the Fermi level. Zh. éksp. Teor. Fiz. 114, 985–1005 (September 1998)     

Interlayer magnetotransport study in electron-doped Sm2−x Ce x CuO4−δ

Vortex and pseudogap states in electron-doped Sm_2−x Ce _x CuO_4−δ (x ∼ 0.14) are investigated by the interlayer transport in magnetic fields up to 45 T. To extract intrinsic properties, we fabricated small 30 nm-high mesa structures, sufficiently thin to be free of the recently reported partial decomposition problems. On cooling, the c-axis resistivity ρ_c of the mesa structures reveals a semiconductive upturn above T_c, followed by a sharp superconducting transition at 20 K. When the magnetic fieldH is applied along the c-axis, ρ_c(T) shows a parallel shift without significant broadening, as also observed in the hole-doped underdoped cuprates. Above the transition we observe negative magnetoresistance (MR), which can be attributed to the field suppression of the pseudogap, whose magnitude is as small as 38 K. Our results in thex ∼ 0.14 samples closely correspond to the interlayer transport behavior in the ‘overdoped’ regime of hole-doped Bi₂Sr₂ CaCu₂ O_8+y.     

Effect of interlayer tunneling on the electronic structure of bilayer cuprates and quantum phase transitions in carrier concentration and high magnetic field

We present a theoretical study of the electronic structure of bilayer HTSC cuprates and its evolution under doping and in a high magnetic field. Analysis is based on the t-t′-t″-J* model in the generalized Hartree-Fock approximation. Possibility of tunneling between CuO2 layers is taken into account in the form of a nonzero integral of hopping between the orbitals of adjacent planes and is included in the scheme of the cluster form of perturbation theory. The main effect of the coupling between two CuO₂ layers in a unit cell is the bilayer splitting manifested in the presence of antibonding and bonding bands formed by a combination of identical bands of the layers themselves. A change in the doping level induces reconstruction of the band structure and the Fermi surface, which gives rise to a number of quantum phase transitions. A high external magnetic field leads to a fundamentally different form of electronic structure. Quantum phase transitions in the field are observed not only under doping, but also upon a variation of the field magnitude. Because of tunneling between the layers, quantum transitions are also split; as a result, a more complex sequence of the Lifshitz transitions than in single-layer structures is observed.     

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)     

Tunneling investigations of single crystals of the single-layer cuprate Bi2Sr2CuOz in high magnetic fields

The coexistence of a superconducting gap and a normal-state gap (pseudogap) is observed in tunneling experiments with high-quality single crystals of the single-layer cuprate Bi₂Sr₂CuO_z. At temperatures T< T _c the normal-state gap, whose width is close to that of the super-conducting gap, does not vanish in magnetic fields H>H _c2. The large smearing of the gap structure in the tunneling spectra and the high conductance of tunnel junctions at zero bias voltage are due to the strong angular dependence of the superconducting-and normal-state gaps. The results of the investigations are in good agreement with recently published angle-resolved photoemission data. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 217–222 (10 August 1998)     

Spin susceptibility of neutron-irradiation-disordered YBa2Cu3O6.9 in the normal and superconducting states

The spin-spin relaxation rate ⁶³ T ₂ ⁻¹ of ⁶³Cu nuclei in CuO₂ layers is measured in the normal and superconducting states of the compound YBa₂Cu₃O_6.9 (T _c ^onset =94 K) subjected to radiation-induced disordering by a fast-neutron flux Φ to T _c ^onset =68 K (Φ=7×10¹⁸ cm⁻²) and T _c ^onset <4 K (Φ=12×10¹⁸ cm⁻²). It is found that as the structural disorder increases, the contribution of the indirect spin-spin interaction ⁶³ T _2G ⁻¹ , which is related to the value of the spin susceptibility at the boundary of the Brillouin zone of the copper planes χ_s(q={π/a; π/a}), decreases slightly at the transition to the superconducting state for the initial sample and remains unchanged for the weakly disordered sample. This behavior of the short-wavelength contribution to the spin susceptibility attests to the stability of the x ²−y ² symmetry of the energy gap against structural disorder, in accordance with proposed theoretical models of Cooper pairing for high-T _c cuprates. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 172–177 (10 February 1998)     

Insulator-metal transition in the single-crystal high-T c superconductor Bi-2201

Variations in the temperature behavior of resistivity, ρ(T), in the ab plane of the anisotropic single-crystal high-T _c superconductor BiSrCuO (2201 phase) have been observed at the insulator-metal (IM) transition. At low temperatures, as one approaches the transition, the Mott relation for two dimensions, ln ρ ∝ T ^−1/3, changes to ln ρ ∝ T ^−1/2, which corresponds to hopping conduction with a Coulomb gap in the density of states. Negative temperature slopes were revealed in the samples near the transition. Estimates suggest that superconductivity in these samples sets in from the Anderson insulator state. The behavior of the width of the superconducting transition and of the temperature of its onset, T _con, at the IM transition has been studied from measurements of the ac magnetic susceptibility. It is shown that in the vicinity of the IM transition the superconducting transition becomes broader, and the onset of the transition T _con shifts toward higher temperatures. This behavior is attributed to nonuniform superconductivity resulting from formation in the crystal of superconducting droplets with different values of T _c , which is caused by fluctuations in the local density of states due to the inherent disorder in the crystal. In these conditions, superconductivity has a percolation character. Fiz. Tverd. Tela (St. Petersburg) 40, 1190–1194 (July 1998)     

Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection

In cuprates, in a view where pairing correlations set in at the pseudogap energy scale T* and acquire global coherence at a lower temperature T_c, the regionT _c⪯ T ⪯ T* is a vast fluctuation regime.T _c andT* vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field H_c2 bounding the superconducting response and the pseudogap closing field H_pg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi₂Sr₂CaCu₂O_8+y report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scaleT* upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the ‘dome’ that coincides with the usual unique upper critical field H_c2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.     

Nature of low-energy excitations in La<Subscript>1.87</Subscript>Sr<Subscript>0.13</Subscript>CuO<Subscript>4</Subscript> superconducting cuprate

The spectra of the conductivity and dielectric constant of La_1.87Sr_0.13CuO₄ cuprate have been directly measured in the frequency range of 0.3 to 1.2 THz (10–40 cm⁻¹) and the temperature range of 5 to 300 K in the E | c polarization (the electric field vector of radiation is perpendicular to the copper-oxygen planes). Excitation has been observed in the superconducting phase, and its nature has been attributed to the transverse optical excitation of the condensate of Cooper pairs, which appears because Josephson junctions between CuO planes are modulated due to in-plane magnetic and charge stripes. Additional quasiparticle absorption of unknown origin has been detected at frequencies below ≈15 cm⁻¹ at liquid helium temperatures.     

Rare t-quark decays t → clj+lk? and t → c?jvk induced by doublets of scalar leptoquarks within the minimal four-color-symmetry model

The rare t-quark decays t → cl _j ⁺ l _k ⁻ and t → cṽ _j k _k induced by scalar-leptoquark doublets are considered within the minimal model involving four-color quark-lepton symmetry and the Higgs mechanism of quark and lepton mass splitting. The partial widths with respect to the decays being considered and the total widths Γ(t → cl ⁺′l ⁻) = Σ_j,k Γ(t → cl _j ⁺ l _k ⁻ ) and Γ(t → cl ⁺′l ⁻) = Σ_j,kΓ(t → cṽ _j v _k ) with respect to, respectively, the charged leptonic and neutrino modes are calculated. It is shown that, at scalar-leptoquark masses higher than the t-quark mass (m _S > m _t), the branching ratios for these modes are Br(t → cl ⁺′l ⁻) ≈ (3.5−0.4) × 10⁻⁵ and Br(t → cṽ′v) ≈ (7.1−0.8) × 10⁻⁵ at m _s = 180–250 GeV and an appropriate value of the leptoquark-mixing angle (sin β ≈ 0.2) and can increase for m _S < m _t to Br(t → cl ⁺′l ⁻) ≈ 0.03−0.002 and Br(t → cl ⁺′l ⁻) ≈ 0.46−0.05 for the charged mode at m _S = 150–170 GeV for sin β ≈ 1 and sin β ≈ 0.2, respectively. In the cases being considered, t-quark decays to pairs of charged leptons can be accessible to detection at LHC. In the last case, these decays could manifest themselves (for example, in dilepton events) at the Tevatron as well. Original Russian Text ? P.Yu. Popov, A.D. Smirnov, 2006, published in Yadernaya Fizika, 2006, Vol. 69, No. 6, pp. 1006–1016.     

Characteristic features of d pairing in bilayer cuprates under conditions of Peierls instability of the normal phase

A system of self-consistent integral equations for the superconducting gap is formulated and solved taking account of the instability of the normal phase of bilayer cuprates against charge-density waves. The critical parameters are calculated as a function of the wave vector, temperature, and doping index. It is found that the region in which superconductivity coexists with d-type charge-density waves depends strongly on the doping index. The effective energy-gap parameter, determined as the interval between the peaks of the density of states, can have a local minimum at temperatures T<T _c . Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 583–587 (10 October 1998)     

Superconducting current in hybrid structures with an antiferromagnetic interlayer

It is shown experimentally that the superconducting current density in Nb/Au/Ca_{1 − x} Sr _x CuO₂/YBa₂Cu₃O_{7 − δ} hybrid superconducting heterostructures with a Ca_{1 − x} Sr _x CuO₂ anti-ferromagnetic (AF) cuprate interlayer is anomalously high for interlayer thicknesses d _M = 10–50 nm and the characteristic damping length for superconducting correlations is on the order of 10 nm. The experimental results are explained on the basis of theoretical analysis of a junction of two superconductors (S′ and S) connected by a magnetic multilayer with the AF ordering of magnetization in the layers. It is shown that with such a magnetization ordering, anomalous proximity effect determined by the singlet component of the condensate wavefunction may take place. As a result, the critical currents in S′/I/AF/S and S′/I/N/S structures (I denotes an insulator, and N, the normal metal) may coincide in order of magnitude even when the thickness of the AF interlayer considerably exceeds the decay length of the condensate wavefunction in ferromagnetic layers.     

Discrete nature of superconducting nanochannels in the cuprate pseudogap regime at <Emphasis Type="Italic">T</Emphasis> > 200 K

Intensification of segregation processes with a decrease in the charge carrier concentration in cuprates should lead, according to the string model, to a decrease the discrete width w _ν of dominant bosonic stripes and an increase in their critical temperature T _c up to 1200 K. A comparison of the simulated results with the experimental data gives grounds to conclude that the anomalies of the electronic properties observed in the pseudogap regime of lightly dopes cuprates are most likely to be due to the formation of a metastable network of superconducting nanochannels with T _c > 200 K from the bosonic stripes limited by w _ν ≤ 2 nm.