Two Domains of the Parameter Space of the 2D Hubbard Model for High-Tc Superconductors

High-T _c superconducting cuprates have two types of Fermi surfaces: simple-2D-tight-binding-band type (LSCO type) and the much deformed one (Bi2212 type). The difference is attributed to that of band parameter values, i.e., t′ ∼ −0.1 and t″ ∼ 0 versus t′ ∼ −0.3 and t″ ∼ 0.2 in terms of the second- and third-neighbor transfer energies t′ and t″, respectively (energy unit is the nearest-neighbor transfer energy t). Assuming a moderate value of on-site Coulomb energy U ∼ 6 and performing the variational Monte Carlo computation, we found that the two superconducting parameter domains exist in fact around these parameter sets, respectively, in which superconductivity predominates over spin density wave (SDW) due to the latter being at the brink of vanishing. Stripes were obtained in the first domain but tend to disappear in the second. In the latter domain there seems to exist parameter sets for which superconductivity appears without doping.     

The Maximum Levitation Force of High-T c Superconductors

In this paper we present the dependence of the maximum levitation force (F _z ^max) of a high-T _c superconductor (HTS) on the structural factors of high-T _c superconducting systems based on the Bean critical state model and Ampère’s law. A transition point of the surface magnetic field (B _s ) of a permanent magnet (PM) is found at which the relation between F _z ^max and B _s changes: while the surface magnetic field is less than the transition value the dependence is subject to a nonlinear function, otherwise it is a linear one. The two different relations are estimated to correspond to partial penetration of the shielding currents inside the superconductor below the transition point and complete penetration above it respectively. The influence of geometric properties of superconductors on the dependence is also investigated. In addition, the relation between F _z ^max and the critical current density (J _c ) of the HTS is discussed. The maximum levitation force saturates at high J _c . An optimum function of the J _c and the B _s is presented in order to achieve large F _z ^max.      

Effect of Normal-State Pseudogap on Physical Quantities in Hubbard Model for Underdoped High-T c Cuprates

We develop the strong-coupling theory of coexisting charge-density-wave (CDW) and superconductivityd-wave gaps within the framework of the FLEX (fluctuation exchange) approximation for the two-dimensional Hubbard model. For nested sections of the Fermi surface these equations reduce to the previous FLEX equations for superconductivity where the squared energy gap _s ² in the denominator of the Green's function is replaced by ( _s ² + _c ² ) (here _s is the superconductivity and _c the CDW gap). We solve these equations by taking for _c a phenomenologicald-wave gap. The resulting neutron scattering intensity, spin-lattice relaxation rate 1/T₁ , Knight shift, resistivity, and photoemission intensity are in qualitative agreement with the data on underdoped high-T_c cuprates. TheT_c for superconductivity decreases and the crossover temperature T_* for 1/T₁Tincreases with increasing gap amplitude of _c which is in qualitative agreement with the phase diagram for underdoped cuprates.     

Dynamical Phase Diagram of Driven Vortices in High-T c Superconductors

Large-scale simulations on the current-driven three-dimensional frustrated anisotropic XY model with resistively-shunted junction dynamics have been performed to study the dynamical phase diagram in high-T _c superconductors. With the decrease of the current, a moving smectic is found between a moving Bragg glass and a moving liquid at high temperatures. The first-order phase transition between the moving Bragg glass and the moving smectic is clarified. At low temperatures, the moving Bragg glass can crossover to the (creeping) Bragg glass directly. Interestingly, at very high currents, the moving Bragg glass is replaced by a highly disordered phase due to the activation of vortices and anti-vortices.     

Critical Behavior in the Low-Energy Spin Fluctuations in High-T c Superconductors

We study the spin fluctuations of pure and Zn-substituted La_{2 ? x} Sr _x CuO₄ using the muon spin relaxation technique. Superconductivity is found to coexist with low-frequency spin fluctuations over a large region of the superconducting phase diagram. The characteristic temperature of spin fluctuations detected by μSR decreases with increasing x and vanishes above a critical doping x _c ≈ 0.19. This value of x _c coincides with the doping at which the normal state pseudogap extrapolates to zero. These results are discussed in terms of a quantum transition that separates the superconducting phase diagram of high-temperature superconductors into two distinct ground states.     

Effect of Interlayer Interaction on the Specific Heat of High-T c Superconductors

The effect of interlayer interactions on the electronic specific heat of high-T _c layered superconductors has been studied within the framework of the Hirsch model. In the present paper we extend our previous work in order to evaluate the expression for specific heat. It is shown that the inclusion of interlayer interactions suppresses the height of the jump in the specific heat at T _c.     

Mechanism of the Dynamic Thermal Expansion of Bismuth-Based High-T c Superconductors1

The dynamic process of thermal expansion (DPTE) of Bi-based high-T _c (HTC) superconductor samples (Bi₂ Sr₂ Ca₂ Cu₃ O₁₀, T _c=105K) is studied theoretically. The abnormal expansion behavior in the superconducting and normal states are of relevance to the energy absorption and pairing mechanisms.     

The 2D Hubbard Model and the High T c Cuprate Problem

Numerical calculations are being used to explore both the properties of strongly-correlated electron systems and the interactions which give rise to these properties. Here, we review what has been learned about the two-dimensional (2D) Hubbard model and comment on its relationship to the high T _c cuprate problem.     

Study of Superconducting Properties in Bismuth-Based Cerium Doped High-T c Superconductors

Superconductivity in bismuth-based high-T _c superconducting materials attracts the researchers for their unique properties. Bismuth-based superconductors commonly called BSCCO have great importance among the superconducting family. These are divided into three phases among them 2223 phase is highly studied in order to investigate its superconducting properties by substitution of different elements. We have studied the substitution of cerium (Ce) on the calcium site of bismuth-based Bi(Pb)Sr(Ba)-2223 high-T _c superconductor. The nominal compositions of Bi_1.6Pb_0.4Sr_1.6Ba_0.4(Ca_1?x Ce _x )₂Cu₃O _x ceramic superconductor were prepared by the sol–gel method. X-ray diffraction (XRD) was done at room temperature for structural analysis and different parameters were calculated. Surface morphology was done by scanning electron microscopy (SEM). DC resistivity measurements for the transition temperature of synthesized superconducting samples were taken by the standard four-probe method, apparatus for which was developed in our laboratory. Current density measurements were also taken by the same apparatus. The synthesized superconducting samples were also characterized by thermogravimetric analysis (TG) and Fourier transformation infrared radiations (FTIR). It is observed that the substitution of cerium on the calcium site favors the formation of single high-T _c 2223 phase.     

Lorentz Microscopy Observation of Unconventional Behaviors of Vortices in High-T c Superconductors

Vortices in high-T _c superconductors have been predicted to behave in unconventional manners that reflect the layered structure of the materials. Our newly developed 1-MV field-emission electron microscope has opened the way to enable individual vortices to be observed inside high-T _c superconducting thin films. This makes it possible to investigate the inner structures of vortices, such as those trapped along tilted columnar defects and those of chain vortices that are formed when a magnetic field is obliquely applied with respect to the normal of the layer plane of the materials.     

Polarized Electronic Raman Scattering Studies of Underdoped and Overdoped High-T c Superconductors

We report on polarized Raman scattering from high-T _c superconductors in the Bi ₂ Sr ₂ CaCu ₂ O ₈₊ (Bi2212) and HgBa ₂ CuO ₄₊ (Hg1201) classes, with an emphasis on the effect of superconductivity on the low frequency electronic continuum. The Hg-based materials confirm earlier observations from Bi2212 that the superconducting energy gap 2 peak is not present in underdoped samples, while its Raman shift is maximum in B _1g symmetry at optimal doping, and decreases dramatically with overdoping. These similarities despite the different numbers of bands crossing the Fermi surface argues against a multiple-band explanation for the anomalous doping dependence of the gap. We also discuss an anomalous B _1g feature observed at 600 cm ^–1 in Y underdoped Bi2212. This pseudogap-like feature has several properties which suggest it is of electronic - rather than phononic - origin.     

Pinning of Stripes by Local Structural Distortions in Cuprate High-T c Superconductors

We study the spin-density wave (stripe) instability in lattices with mixed low-temperature orthorhombic (LTO) and low-temperature tetragonal (LTT) crystal symmetry. Within an explicit mean-field model, it is shown how local LTT regions act as pinning centers for static stripe formation. We calculate the modulations in the local density of states near these local stripe regions and find that mainly the coherence peaks and the van Hove singularity (VHS) are spatially modulated. Lastly, we use the real-space approach to simulate recent tunneling data in the overdoped regime where the VHS has been detected by utilizing local normal state regions.     

Quantized Vortices and Diamagnetic Precursor to the Meissner State in High-T c Superconductors

We report the magnetic imaging for underdoped and optimally-dopedLa_2–x Sr _x CuO₄ (LSCO) thin films on single substrates and nearly optimallydoped YBa₂Cu₃O_7–x (YBCO) thin films on tricrystal substrates in the temperature range both below and above T _c using scanning SQUID microscopy. Below T _c, clear integer- and half-integer quantized vortices were observable. Above T _c, however, the inhomogeneous diamagnetic domains appeared. The local diamagnetic domains that led to the Meissner state were found in the broad temperature range for underdoped samples and in the narrow limited temperature range for optimally-doped samples. The results provide evidence that local diamagnetic domains are closely related to the pseudogap state. The continuous connection of the domain state above T _c with the state of a half-integer vortex at the tricritical point in the YBCO film below T _c also indicates that the diamagnetic domains are also closely related to the occurrence of d_x ^{2-y 2}-wave superconductivity.     

Effects of the Experimental Geometry on the Vortex Dynamics in High-T c, Superconductors

A brief overview is given on the macroscopic electrodynamics of type-II superconductors with and without vortex pinning, of various shapes and in an applied magnetic field, but also with applied transport current and with finite London penetration depth . The extension to >0 is important at low inductions B to describe the transition to the Meissner state, and for films with thickness not much larger than . The finite width of the surface layer with screening currents and the correct dc and ac responses in various geometries follow from an equation of motion for the current density, with a dependent integral kernel.     

Frustrated Phase Separation in the Overdoped Regime of “123” High-T c Superconductors

Recent inelastic neutron scattering measurements revealed the crystal-field (CF) spectra of the overdoped R_{1 ? y} Ca_yBa₂Cu₃O_≈7 (R = Ho, Er; 0 < y < 0.25) high-T _c superconductors to consist of two spectral components associated with the optimally doped and the overdoped domains. Increase of the Ca concentration does not affect the local charge density of domains, but changes the spectral weight of the components. In the sense of this “two-phase” picture, which was established earlier for the underdoped region, there is a smooth crossover between the under- and overdoped parts of the phase diagram. The charge origin of the observed superposition effect is confirmed by the systematic analysis of the concentration dependences of the CF parameters for both Ho- and Er-based compounds. Therefore, the local charge inhomogeneity in the CuO₂ planes of high-T _c cuprates is a characteristic feature of the doping process, which depends neither on the way to introduce doping nor on the doping level.     

Pinning Effects in Vortex States of High-T c Superconductors: Monte Carlo Simulations

Large scale Monte Carlo simulations are performed in order to clarify thermodynamic properties of interlayer Josephson vortices induced by a magnetic field parallel to the ab plane of high-T _c superconductors. It is revealed that there is a tricritical point in the B–T phase diagram, so that for magnetic field above (below) this point the normal to superconductivity transition is continuous (discontinuous). The critical point is described by the product of the magnetic field and the c-axis anisotropy parameter. The origin of the change in the nature of phase transition is the intrinsic pinning effect of the layer structure.     

Thermodynamics of the Frustrated 2D Hubbard Model

The thermodynamic properties of the quarter filled 2D Hubbard model extended by next-nearest-neighbor (NNN) hopping have been studied in an exact diagonalization method on a tilted square cluster. The NNN hopping interaction (i.e. frustration) is prominent at the low-temperature region. A positive (negative) diagonal hopping t′ favors (suppresses) double occupancy and hence decreases (increases) local moment. At higher temperatures thermal excitations favor the formation of doublans against the strong Coulomb repulsion U and the weak diagonal hopping, hence decreasing local moment. A two-peak structure is observed in the specific heat curves with the inclusion of negative NNN hopping. The low-T peak in specific heat is highly suppressed in comparison to the high-T peak. It has also been argued that t′ influences the ‘pseudogap’ energy scale. In the present case of quarter filling, a weak and short range antiferromagnetic order is present at very low temperatures, which is slightly suppressed (enhanced) by positive (negative) t′. The effect of t′ is more pronounced in the non-interacting limit.     

An Overview on the Research of Iron-Based High-T c Superconductors Probed by X-ray Absorption Spectroscopy

The discovery in 2008 of a new family of high-T _c superconductor (HTSC), i.e., layered compounds based on iron, has spurred a tremendous interest in the community of condensed matter physics. This discovery has broken cuprate “monopoly” in the physics of HTSC materials. Until now, thousands of experimental and theoretical methods were devoted to investigate the superconducting properties of this new iron-based HTSCs. Synchrotron radiation-based X-ray absorption spectroscopy (XAS) made great contributions to the local lattice structure, the electronic structure, and even the superconductive mechanism of this iron-based materials. The aim of this review is a short introduction into the progress of research on new iron-based HTSCs probed by the unique technique—XAS, including the electron correlations, local lattice distortions, changes of valence upon doping or pressure, and even the isotope effect for this new iron-based family.     

The Role of Weak Links and Zn-Doping on Magnetic Parameters of High-T c Superconductors

The second harmonic signal, which is generated by co-application of AC and DC fields to polycrystalline type-II superconductors, were analyzed in terms of the weak links and the critical current density. With this aim the YBa₂Cu_3?x Zn _x O_7?y (x=0, 0.01, 0.02, 0.03, 0.05, and 0.1) samples were synthesized in order to adjust intergranular couplings and thus the strength of weak links. The mechanical and magnetic measurements are in good agreement on that Zn doping reduces strength of the links between grains; however, contrary to the common expectations, it has no direct contribution to the 2nd harmonic signal strength.     

Ground-State Properties of the Frustrated 2D Quarter-Filled Hubbard Model

The Hubbard model extended by next-nearest-neighbor (NNN) hopping t′ at quarter filling has been investigated numerically using exact diagonalization technique on a small cluster. We report the role of frustration (NNN hopping) on the ground-state properties of the system. The effects of both positive and negative t′ are considered. Results show that a short range antiferromagnetic order is present in the system, which is favored (suppressed) by negative (positive) t′. It appears that electron-electron correlation decreases with NNN hopping interaction. Inclusion of t′ facilitates electron hopping. Though pairing in the extended s-wave channel is dominant for quarter-filled unfrustrated system, d-wave pairing becomes dominant with the inclusion of negative t′.