Antinodal Points Research Articles

Origin of the pseudogap in cuprate superconductors from quantum cluster theories

We analyze the origin of the pseudogap present in cuprate superconductors. We elucidate the mechanism of pseudogap formation close to the Mott localization within the dynamical cluster approach (DCA) to the Hubbard model. As the Coulomb interaction is increased, cluster–bath Kondo states are destroyed and a nondegenerate bound cluster state is formed, leading to a pseudogap. This occurs first at the antinodal point due to its weaker coupling to the bath, explaining the momentum dependence of the pseudogap. We find that the character of the pseudogap is related to breaking d-wave pairs.

Many-body effects in high-Tc materials: anomalous properties in the pseudogap region

Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green’s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation nT and temperature is calculated. At low temperatures, the susceptibility presents a peak for nT ≃ 0.80. The results suggest that it is the onset of short-range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function , is presented for different dopings. It has been observed that above nT ≃ 0.80 the ordinary Fermi surface evolves to a hole pocket with pseudogaps near the antinodal points (0,π) and (π,0).

SPECTRAL FUNCTION OF A d-p HUBBARD MODEL

This work investigates a d-p Hubbard model by the n-pole approximation in the hole-doped regime. In particular, the spectral function A(ω, k) is analyzed varying the filling, the local Coulomb interaction and the d-p hybridization. It should be remarked that the original n-pole approximation (Phys. Rev.184, 451 1969) has been improved in order to include adequately the k-dependence of the important correlation function 〈Sj·Si〉 present in the poles of the Green's functions. It has been verified that the topology of the Fermi surface (defined by A(ω = 0, k)) is deeply affected by the doping, the strength of the Coulomb interaction and also by the hybridization. Particularly, in the underdoped regime, the spectral function A(ω = 0, k) presents very low intensity close to the antinodal points (0, ±π) and (±π, 0). Such a behavior produces an anomalous Fermi surface (pockets) with pseudogaps in the region of the antinodal points. On the other hand, if the d-p hybridization is enhanced sufficiently, such pseudogaps vanish. It is precisely the correlation function 〈Sj·Si〉, present in the poles of the Green's functions, plays an important role in the underdoped situation. In fact, antiferromagnetic correlations coming from 〈Sj·Si〉 strongly modify the quasiparticle band structure. This is the ultimate source of anomalies in the Fermi surface in the present approach.

Melting of stripe phases and its signature in the single-particle spectral function

Motivated by the recent experimental data [Phys. Rev. B 79, 100502 (2009)] indicating the existence of a pure stripe charge order over unprecedently wide temperature range in La_{1.8-x}Eu_{0.2}Sr_xCuO_4, we investigate the temperature-induced melting of the metallic stripe phase. In spite of taking into account local dynamic correlations within a real-space dynamical mean-field theory of the Hubbard model, we observe a mean-field like melting of the stripe order irrespective of the choice of the next-nearest neighbor hopping. The temperature dependence of the single-particle spectral function shows the stripe induced formation of a flat band around the antinodal points accompanied by the opening a gap in the nodal direction.

Capillary wave motion excited by high frequency surface acoustic waves

This paper presents a numerical and experimental study of capillary wave motion excited by high frequency surface acoustic waves (SAWs). The objective of this study is to provide insight into the dynamic behavior of the fluid free surface and its dependence on the excitation amplitude. A two-dimensional numerical model that couples the motion of the piezoelectric substrate to a thin liquid layer atop the substrate is constructed. A perturbation method, in the limit of small-amplitude acoustic waves, is used to decompose the equations governing fluid motion to resolve the widely differing time scales associated with the high frequency excitation. While this model focuses on the free surface dynamics in the low-amplitude flow regime, the experimental study focuses on the high-amplitude flow regime. Transformation of time series data from both experiments and simulations into the frequency domain reveals that, in the low-amplitude regime, a fundamental resonant frequency and a superharmonic frequency are found in the frequency spectra. The former is found to be identical to that of the applied SAW, and the free surface displacement magnitude is comparable to that of the substrate displacement. Our numerical results also confirm previous speculation that the separation distance between two displacement antinodal points on the free surface is δSt≈λSAW/2 for a film and δSt≈λf/2 for a drop, where λSAW and λf denote the SAW wavelength and the acoustic wavelength in the fluid, respectively. Finally, in the high-amplitude regime, strong nonlinearities shift the acoustic energy to a lower frequency than that of the SAW; this low-frequency broadband response, quite contrary to the subharmonic half-frequency capillary wave excitation predicted by the classical linear or weakly nonlinear Faraday theories, is supported by a scaling analysis of the momentum equations.

COOPERATIVE LOCALIZATION-DELOCALIZATION IN THE HIGH Tc CUPRATES

The intrinsic metastable crystal structure of the cuprates results in local dynamical lattice instabilities, strongly coupled to the density fluctuations of the charge carriers. They acquire in this way simultaneously both, delocalized and localized features. It is responsible for a partial fractioning of the Fermi surface, i.e., the Fermi surface gets hidden in a region around the anti-nodal points, because of the opening of a pseudogap in the normal state, arising from a partial charge localization. The high energy localized single-particle features are a result of a segregation of the homogeneous crystal structure into checker-board local nano-size structures, which breaks the local translational and rotational symmetry. The pairing in such a system is dynamical rather than static, whereby charge carriers get momentarily trapped into pairs in a deformable dynamically fluctuating ligand environment. We conclude that the intrinsically heterogeneous structure of the cuprates must play an important role in this type of superconductivity.

Finite element analysis and experiments on a silicon membrane actuated by an epitaxial PZT thin film for localized-mass sensing applications

In this paper, we investigate the performance of a piezoelectric membrane actuated by an epitaxial piezoelectric Pb(Zr 0.2Ti 0.8)O 3 (PZT) thin film for localized-mass sensing applications. The fabrication and characterization of piezoelectric circular membranes based on epitaxial thin films prepared on a silicon wafer are presented. The dynamic behavior and mass sensing performance of the proposed structure are experimentally investigated and compared to numerical analyses. A 1500 μm diameter silicon membrane actuated by a 150 nm thick epitaxial PZT film exhibits a strong harmonic oscillation response with a high quality factor of 110–144 depending on the resonant mode at atmospheric pressure. Different aspects related to the effect of the mass position and of the resonant mode on the mass sensitivity as well as the minimum detectable mass are evaluated. The operation of the epitaxial PZT membrane as a mass sensor is determined by loading polystyrene microspheres. The mass sensitivity is a function of the mass position, which is the highest at the antinodal points. The epitaxial PZT membrane exhibits a mass sensitivity in the order of 10 −12 g/Hz with a minimum detectable mass of 5 ng. The results reveal that the mass sensor realized with the epitaxial PZT thin film, which is capable of generating a high actuating force, is a promising candidate for the development of high performance mass sensors. Such devices can be applied for various biological and chemical sensing applications.

Cardinal points and generalizations

In the presence of astigmatism a focal point typically becomes the well-known interval of Sturm with its pair of axially-separated orthogonal line singularities. The same is true of nodal points except that the issues are more complicated: a nodal point may become a nodal interval with a pair of nodal line singularities, but they are not generally orthogonal, and it is possible for there to be only one line singularity or even none at all. The effect of astigmatism on principal points is the motivation behind this paper. The three classes of cardinal points are defined in the literature in a disjointed fashion. Here a unified approach is adopted, phrased in terms of rays and linear optics, in which focal, nodal and principal points are defined as particular cases of a large class of special structures. The special structures arising in the presence of astigmatism turn out to be described by mathematical expressions of the same form as those that describe nodal structures. As a consequence everything that holds for nodal points, lines and other structures now extends to all other special points as well, including principal points and the lesser-known anti-principal and anti-nodal points. Thus the paper unifies Gauss's and Listing's concepts of cardinal points within a large class of special structures and generalizes them to allow for refracting elements which may be astigmatic and relatively decentred. A numerical example illustrates the calculation of cardinal structures in a model eye with astigmatic and heterocentric refracting surfaces.

Crossover region between nodal and antinodal states at the Fermi level of optimally doped and overdopedBi2Sr1.6Nd0.4CuO6+δ

We have studied Bi$_{2}$Sr$_{1.6}$Nd$_{0.4}$CuO$_{6+\delta}$ using Angle Resolved Photoemission Spectroscopy in the optimal and overdoped regions of the phase diagram. We identify a narrow crossover region in the electronic structure between the nodal and antinodal regions associated with the deviation from a pure d-wave gap function, an abrupt increase of the quasiparticle lifetime, the formation of Fermi arcs above T$_c$, and a sudden shift of the bosonic mode energy from higher energy, $\sim${60meV}, near the nodal direction, to lower energy, $\sim${20meV}, near the antinodal direction. Our work underscores the importance of a unique crossover region in the momentum space near E$_F$ for the single layered cuprates, between the nodal and antinodal points, that is independent of the antiferromagnetic zone boundary.

Boson-fermion duality and metastability in cuprate superconductors

The intrinsic structural metastability in cuprate high T$_c$ materials, evidenced in a checker-board domain structure of the CuO$_2$ planes, locally breaks translational and rotational symmetry. Dynamical charge - deformation fluctuations of such nano-size unidirectional domains, involving Cu-O-Cu molecular bonds, result in resonantly fluctuating diamagnetic pairs embedded in a correlated Fermi liquid. As a consequence, the single-particle spectral properties acquire simultaneously (i) fermionic low energy Bogoliubov branches for propagating Cooper pairs and (ii) bosonic localized glassy structures for tightly bound states of them at high energies. The partial localization of the single-particle excitations results in a fractionation of the Fermi surface as the strength of the exchange coupling between itinerant fermions and partially localized fermion pairs increases upon moving from the nodal to the anti-nodal point. This is also the reason why, upon hole doping, bound fermion pairs predominantly accumulate near the anti-nodal points and ultimately condense in an anisotropic fashion, tracking the gap in the single particle spectrum.

Microscopic approach to high-temperature superconductors within the t-J model

Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature ${T}_{c}$ is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have $d$-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.

Interplay between antiferromagnetism and superconductivity in the Hubbard model with frustration

Coexistence of and competition between antiferromagnetism (AF) and d-wave superconductivity (SC) are studied for a Hubbard model on the square lattice with a diagonal transfer t ′ , using a variational Monte Carlo method. The following improvements are introduced into the trial function: (1) Coexistence of AF and d-wave singlet gaps that allows a continuous description of their interplay, (2) band renormalization effect, and (3) refined doublon–holon correlation factors. Optimizing this function for a strongly correlated value of U / t , we construct a phase diagram in the δ (doping rate)- t ′ / t space, and find that for t ′ / t ⩾ - 0.15 a coexisting state is realized, whose range of δ extends as t ′ / t increases. In contrast, for t ′ / t = - 0.3 , AF and SC states are mutually exclusive, and a coexisting state does not appear. In connection with the “two-gap” problem, we confirm even for the present refined function that the gradient of momentum distribution function at the antinodal point mainly dominates the magnitude of the d-wave SC correlation function.

Self-trapping and Binding of Particles from Singular Pockets in Weakly Doped AFM Mott Insulator

We consider effects of binding and self-trapping of particles added or excited over the insulating state of an antiferromagnetic Mott insulator. The state of an electron or a hole (as appears in ARPES), or of their bound pair (as appears in optics) can be modified by interactions with collective degrees of freedom—deformations of the lattice or of the spin environment. The resulting self-localized state lowers the total particle energy, enhances its effective mass and splits off the electronic level below the nominal insulating gap. We show theoretically that the effect is particularly pronounced for states near the antinodal (π, 0) type point of the Brillouin zone of the CuO2 because of proximity to the van Hove singularity. We study also the van Hove enhancements for bound states of the electron with neutral and charged impurities and for inter-gap excitons. The results are clearly important for undoped and electron-doped cuprates where the antinodal points correspond to the spectrum bottom for electrons. The effect is indirectly important for lightly hole-doped cuprates concerning the ARPES spectrum transfer between the nodal arcs and the dark antinodal regions.

Polarons near Van Hove points in 2D charge or spin density waves

Abstract We study theoretically the effects of impurities and of gap distortions in binding and self-trapping of particles added or excited over the insulating state of an antiferromagnetic Mott insulator. Wave functions of single particles or of bound excitons are affected by interactions with collective degrees of freedom, as shown by ARPES and optics experiments. The resulting self-localized state lowers the total particle energy, enhances its effective mass and splits off the electronic level below the nominal insulating gap. Most of the features measured experimentally in lightly n-doped cuprates are related to electronic states originated by anti-nodal points ( π , 0 ) of the Brillouin zone. In these points the van Hove singularity plays a major role by enhancing bound states of the electron with neutral and charged impurities and of inter-gap excitons.

Evidences of the Charge–Lattice Interaction in Undoped Cuprates

The anomalous temperature dependence of the angle resolved photoemission spectra (ARPES) in undoped cuprates is investigated by using a self-consistent approach within the t-J-Holstein model. The cooperative interplay of coupling of the hole to magnetic fluctuations and strong electron–phonon interaction turns out crucial to explain the experimental data. The model is extended to take into account the longer-range hoppings t′ and t′′. The effect is a large anisotropy of the electron–phonon interaction (EPI) leading to a completely different influence of EPI on the nodal and antinodal points in agreement with the experiments.

Oscillating bubble concentration and its size distribution using acoustic emission spectra

New method has been proposed for the estimation of size and number density distribution of oscillating bubbles in a sonochemical reactor using acoustic emission spectra measurements. Bubble size distribution has been determined using Minnaert’s equation [M. Minnaert, On musical air bubbles and sound of running water, Philanthr. Mag. 16 (1933) 235], i.e., size of oscillating bubble is inversely related to the frequency of its volume oscillations. Decomposition of the pressure signal measured by the hydrophone in frequency domain of FFT spectrum and then inverse FFT reconstruction of the signal at each frequency level has been carried out to get the information about each of the bubble/cavity oscillation event. The number mean radius of the bubble size is calculated to be in the range of 50–80 μm and it was not found to vary much with the spatial distribution of acoustic field strength of the ultrasound processor used in the work. However, the number density of the oscillating bubbles and the nature of the distribution were found to vary in different horizontal planes away from the driving transducer surface in the ultrasonic bath. A separate set of experiments on erosion assessment studies were carried out using a thin aluminium foil, revealing a phenomena of active region of oscillating bubbles at antinodal points of the stationary waves, identical to the information provided by the acoustic emission spectra at the same location in the ultrasonic bath.

The two-component physics in cuprates in the real space and in the momentum representation

Gradual evolution of two phase coexistence between dynamical and static regimes in cuprates is first investigated in the real space by making use of available neutron scattering, NMR and μSR data. Analyses of the Hall effect and the ARPES spectra reveals the presence of two groups of charge carriers in LSCO. The T-dependent component is due to the thermal activation of bound electron-hole structures seen near antinodal points in the Brillouin zone, thus introducing the two component physics also for the momentum representation. Interpretation of so-called ‘van Hove bands’ undergoes drastic changes. Importance of the findings for pseudo-gap physics is stressed. Relation to some recent STM and STS results is discussed.

Nonlocal Composite Spin-Lattice Polarons in High Temperature Superconductors

The nonlocal nature of the polaron formation in t - t '- t'' - J model is studied in large lattices up to 64 sites by developing a new numerical method. We show that the effect of longer-range hoppings t' and t'' is a large anisotropy of the electron-phonon interaction (EPI) leading to a completely different influence of EPI on the nodal and antinodal points in agreement with the experiments. Furthermore, nonlocal EPI preserves polaron's quantum motion, which destroys the antiferromagnetic order effectively, even in the strong coupling regime, although the quasiparticle weight in angle-resolved-photoemission spectroscopy is strongly suppressed.

Importance of the Electron–Phonon Interaction with the Forward Scattering Peak for Superconducting Pairing in Cuprates

We discuss first some basic experimental facts related to ARPES, tunnelling, optics and neutron scattering measurements. They give evidence for the relevance of the electron–phonon interaction (EPI) in pairing mechanism of HTSC cuprates. A controllable and very efficient theory for strong correlations and their effects on EPI is discussed. The theory is based on the 1/N expansion method in the t–J model without using slave bosons (or fermions). The remarkable prediction is that strong correlations renormalize EPI and other charge-fluctuation properties (by including nonmagnetic impurity scattering) in such a way that the forward scattering peak (FSP) appears in the corresponding effective interactions. The existence of FSP in EPI is additionally supported by the weakly screened Madelung interaction in the ionic–metallic structure of layered cuprates. Pronounced FSP in EPI of HTSC cuprates reconciles many puzzling results, which could not be explained by the old theory with the momentum independent EPI. For instance, EPI with FSP gives that the couplings in the s- and d-wave pairing channel are of the same magnitude near and below the optimal hole doping. It is shown that FSP in the impurity scattering potential is responsible for robustness of d-wave pairing in cuprates with nonmagnetic impurities and other defects. The ARPES kink and the isotope effect in the nodal and anti-nodal points, as well as the collapse of the elastic nonmagnetic impurity scattering in the superconducting state, are explained by this theory in a consistent way. The proposed theory also explains why the nodal kink is not-shifted in the superconducting state while the anti-nodal kink is shifted by the maximal superconducting gap. It turns out, that in systems with FSP in EPI besides the classical phase fluctuations there are also internal fluctuations of Cooper pairs. The latter effect is pronounced in systems with long-ranged pairing forees, thus giving rise to an additional contribution to the pseudogap behavior.

Reevaluation of the coupling to a bosonic mode of the charge carriers in(Bi,Pb)2Sr2CaCu2O8+δat the antinodal point

Angle-resolved photoemission spectroscopy (ARPES) is used to study the spectral function of the optimally doped high-T$_c$ superconductor (Bi,Pb)$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ in the vicinity of the antinodal point in the superconducting state. Using a parameterized self-energy function, it was possible to describe both the coherent and the incoherent spectral weight of the bonding and the antibonding band. The renormalization effects can be assigned to a very strong coupling to the magnetic resonance mode and at higher energies to a bandwidth renormalization by a factor of two, probably caused by a coupling to a continuum. The present reevaluation of the ARPES data allows to come to a more reliable determination of the value of the coupling strength of the charge carriers to the mode. The experimental results for the dressing of the charge carriers are compared to theoretical models.