Tuning competing orders in La2-xSrxCuO4 cuprate superconductors by the application of an external magnetic field
J. Chang, Ch. Niedermayer, R. Gilardi, N. B. Christensen, H. M. Ronnow, D. F. McMorrow, M. Ay, J. Stahn, O. Sobolev, A. Hiess, S. Pailhes, C. Baines, N. Momono,… 展开作者
J. Chang, Ch. Niedermayer, R. Gilardi, N. B. Christensen, H. M. Ronnow, D. F. McMorrow, M. Ay, J. Stahn, O. Sobolev, A. Hiess, S. Pailhes, C. Baines, N. Momono, M. Oda, M. Ido, J. Mesot
We report the results of a combined muon spin rotation and neutron scattering study on La2-xSrxCuO4 in the vicinity of the so-called 1/8-anomaly. Application of a magnetic field drives the system towards a magnetically ordered spin-density-wave state, which is fully developed at 1/8 doping. The results are discussed in terms of competition between antiferromagnetic and superconducting order parameters.
We show that the asymmetric tunneling spectrum observed in the cuprate superconductors stems from the existence of a competing order. The competition between the competing order and superconductivity can create a charge depletion region near the surface. The asymmetric response of the depletion region as the function of the external voltage causes the asymmetric tunneling spectrum. The effect is very general in a system which is near the phase boundary of two competing states favoring different carrier densities. The asymmetry which has recently been observed in the point-contact spectroscopy …
We construct a 2-leg ladder model of an Fe-pnictide superconductor and discuss its properties and relationship with the familiar 2-leg cuprate model. Our results suggest that the underlying pairing mechanism for the Fe-pnictide superconductors is similar to that for the cuprates.
We present a minimal model for cuprate superconductors. At the unrestricted mean-field level, the model produces homogeneous superconductivity at large doping, striped superconductivity in the underdoped regime and various antiferromagnetic phases at low doping and for high temperatures. On the underdoped side, the superconductor is intrinsically inhomogeneous and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. The model is applied to calculate experimentally measurable ARPES spectra.
This article presents our perspective on STM measurements by Hoffman et al. (cond-mat/0201348) of the vortex lattice in BSCCO. We discuss implications of these measurements for various theories of the cuprate superconductors.
We investigate the scenario of competing order (CO) induced Fermi arcs and pseudogap in cuprate superconductors. For hole-type cuprates, both phenomena as a function of temperature and doping level can be accounted for if the CO vanishes at $T^{\ast}$ above the superconducting transition $T_c$ and the CO wave-vector Q is parallel to the antinodal direction. In contrast, the absence of these phenomena and the non-monotonic d-wave gap in electron-type cuprates may be attributed to $T^{\ast} < T_c$ and a CO wave-vector Q parallel to the nodal direction.
Angle-dependent studies of the gap function provide evidence for the coexistence of two distinct gaps in hole doped cuprates, where the gap near the nodal direction scales with the superconducting transition temperature $T_c$, while that in the antinodal direction scales with the pseudogap temperature. We present model calculations which show that most of the characteristic features observed in the recent angle-resolved photoemission spectroscopy (ARPES) as well as scanning tunneling microscopy (STM) two-gap studies are consistent with a scenario in which the pseudogap has a non-superconductin…
We develop a theory of normal-metal - superconductor (NS) and superconductor - superconductor (SS) tunnelling in bosonic superconductors with strong attractive correlations taking into account coherence effects in single-particle excitation spectrum and disorder. The theory accounts for the existence of two energy scales, their temperature and doping dependencies, asymmetry and inhomogeneity of tunnelling spectra of underdoped cuprate superconductors.
The nodal $d_{x^2-y^2}$ superconducting gap is a hallmark of the cuprate high T$_c$ superconductors. Surprisingly recent angle-resolved photoemission spectroscopy of deeply underdoped cuprates revealed a nodeless energy gap which is adhered to the Fermi surface. Importantly this phenomenon is observed for compounds across several different cuprate families. In this letter we propose an exciting possibility, namely the fully gapped state is a topological superconductor.
Within the kinetic energy driven superconducting mechanism, we study the interplay between superconductivity and the nodal and antinodal superconducting quasiparticle coherences in cuprate superconductors, and find the s-wave superconducting transition temperature is heavily suppressed by the antinodal superconducting quasiparticle coherence, while the d-wave superconducting transition temperature is enhanced, therefore the antinodal superconducting quasiparticle coherence plays a more crucial role in superconductivity of cuprate superconductors.
We propose a unified description of cuprate and iron-based superconductivity. Consistency with magnetic structure inferred from neutron scattering implies significant constraints on the symmetry of the pairing gap for the iron-based superconductors. We find that this unification requires the orbital pairing formfactors for the iron arsenides to differ fundamentally from those for cuprates at the microscopic level.
This ``Perspective'' briefly reviews recent work showing that a class of organic superconductors have important similarities to the cuprate superconductors: (i) There is competition betweeen superconductivity and antiferromagnetism. (ii) Uncoventional metallic behavior is observed near the metal-insulator transition. A more detailed review and discussion of the appropriate strongly correlated electron model can be found in cond-mat/9802198.
Preformed pairs above $T_c$ and the two-gap scenarios are two main proposals for describing the low doping pseudogap phase of high-$T_c$ cuprates. Very recent angle-resolved photoemission experiments have shown features which were interpreted as evidence for preformed pairs. Here it is shown that those results can be explained also in the context of the two-gap scenario if self-energy effects are considered. The discussion is based on the $d$-CDW theory or the flux phase of the $t-J$ model.
We report extensive muon spin rotation measurements on the lightly doped Y1-xCaxBa2Cu3O6+y compound, which allows us to disentangle the effect of disorder, controlled by random Ca2+ substitution, from that of mere doping. A 3D phase diagram of lightly doped cuprates is accurately drawn, showing that a thermally activated antiferromagnetic phase competes with superconductivity around a quantum critical point, hidden underneath a frozen insulating magnetic state. Disorder suppresses both competing order parameters and unveils the underlying frozen state. Doping and disorder destroy the activated…
We suggest a model for electronic structure of cuprate superconductors that makes it possible to describe evolution of this structure with the doping and provides a new explanation for a number of typical features of cuprates, including the pseudogap and the Fermi arcs. According to this model, the unique electronic structure of cuprates is favorable for the formation of two-atomic negative-U centers (NUCs) and realization of a peculiar mechanism of the electron-electron interaction.
In this Letter, we develop a microscopic theory to describe the close proximity between the insulating antiferromagnetic (AF) order and the d-wave superconducting (dSC) order in cuprates. We show that the cuprate ground states form a configuration of coherent pairing states consisting of extended singlet Cooper pairs and triplet $π$ pairs, which can simultaneously describe AF and dSC orders.
The bulge in the doping dependence of the basal plane area of cuprate superconductors is shown to be an effect of the particular inhomogenous electronic structure created by the dense packing of paired self-protected singlets (PSPS) in CuO_2 lattices.
Recent development in the physics of high-temperature cuprate superconductivity is reviewed, with special emphasis on the phenomena of unconventional and non-universal low-energy excitations of hole- and electron-type cuprate superconductors and the possible physical origin. A phenomenology based on coexisting competing orders with cuprate superconductivity in the ground state appears to provide consistent account for a wide range of experimental findings, including the presence (absence) of pseudogaps and Fermi arcs above the superconducting transition $T_c$ in hole-type (electron-type) cupra…
Present-day angle-resolved photoemission spectroscopy (ARPES) has offered a tremendous advance in the understanding of electron energy spectra in cuprate superconductors and some related compounds. However, in high magnetic field, magnetic quantum oscillations at low temperatures indicate the existence of small electron (hole) Fermi pockets seemingly missing in ARPES of hole (electron) doped cuprates. Here ARPES and quantum oscillations are reconciled in the framework of an impurity band in the charge-transfer Mott-Hubbard insulator.
We propose a finite temperature Landau theory that describes competing orders and interlayer tunneling in cuprate superconductors as an important extension to a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)], where the superconducting transition temperature $T_c$ is defined in three possible ways as a function of the zero temperature order parameter. For given parameters, our theory determines $T_c$ without any ambiguity. In mono- and double-layer systems we discuss the relation between zero temperature order parameter and the associated transition temperature in the pr…
A wave function is proposed for the "$4\times 4$" inhomogeneous structures observed on cuprate superconductors. It is based on the Gutzwiller-RVB technique proposed in recent papers, and consists of a Wigner solid of hole pairs embedded in a sea of d-wave spin singlet pairs. Arguments are given that the nodal quasiparticles may remain unscattered and even superconducting on such a structure.
We develop a theory for light-induced superconductivity in underdoped cuprates in which the competing bond-density wave order is suppressed by driving phonons with light. Close to a bond-density wave instability in a system with a small Fermi surface, such as a fractionalized Fermi liquid, we show that the coupling of electrons to phonons is strongly enhanced at the bond-density wave ordering wavevectors, leading to a strong softening of phonons at these wavevectors. For a model of classical phonons with anharmonic couplings, we show that the combination of strong softening and driving can lea…
We report a scaling relation between $ρ_s(0)$ and the product of the pseudogap temperature $T^{*}$, $σ_{\rm DC}$ and $T_c$, with $T^{*}$ rescaled by the maximum transition temperature $T_c^{\max}$, which holds universally in the entire doping range for the hole-doped cuprates.
In a recent letter, Alexandrov and Zavaritsky propose a model to explain the anomalous Nernst signal observed in the normal state of hole-doped cuprates. The aim of this comment is to recall that one of the main assumptions of the authors regarding the experimental data is false.
The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-…
We report a transport study of nonequilibrium quasiparticles in a high-Tc cuprate superconductor using the transient grating technique. Low-intensity laser excitation (at photon energy 1.5 eV) was used to introduce a spatially periodic density of quasiparticles into a high-quality untwinned single crystal of YBa2Cu3O6.5. Probing the evolution of the initial density through space and time yielded the quasiparticle diffusion coefficient, and both inelastic and elastic scattering rates. The technique reported here is potentially applicable to precision measurement of quasiparticle dynamics, not o…
A Gutzwiller-type variational wave function is proposed for the neutron resonance mode in the cuprate superconductors. An efficient re-weighting technique is devised to perform variational Monte Carlo simulation on the proposed wave function which is composed of linearly superposed Gutzwiller projected Slater determinants. The calculation, which involves no free parameter, predicts qualitatively correct behavior for both the energy and the spectral weight of the resonance mode as functions of doping.
The Josephson coupling between optimally cuprate superconductors separated by a spacer with a finite energy cooperon excitation which contributes to the Josephson coupling strength, is examined. For an underdoped cuprate barrier in its normal state, the YRZ model gives a good description of the temperature dependent enhanced Josephson coupling. A detailed examination of origin of the enhancement shows a significant contribution from the cooperon excitation which is comparable to that from nodal quasiparticles.
An electron-phonon interaction arising from the modulation of the superexchange interaction by phonons is studied within the theoretical framework of Kondo lattices. It is relevant in strongly correlated electron liquids in cuprate oxide superconductors, which lie in the vicinity of the Mott-Hubbard metal-insulator transition. It is enhanced by antiferromagnetic and superconducting fluctuations, which are developed mainly because of the superexchange interaction. When the enhancement of the electron-phonon interaction is large enough, it can explain the softening of phonons and kinks in the qu…
We argue that recently measured downward dispersion of the neutron resonance peak in cuprate superconductors is naturally explained if the resonance is viewed as a spin-1 collective mode in a d-wave superconductor. The reduction of the resonant frequency away from the antiferromagnetic wave vector is a direct consequence of the momentum dependence of the d-wave superconducting gap. When the magnetic correlation length becomes large, the dispersion should become magnon-like, i.e., curve upwards from (pi,pi).
The tunneling spectra of the electron-doped cuprate Pr_2-xCe_xCuO4 as a function of doping and temperature is reported. We find that the superconducting gap, delta, shows a BCS-like temperature dependence even for extremely low carrier concentrations (studied here for the first time). Moreover, delta follows the doping dependence of Tc, in strong contrast with tunneling studies of hole-doped cuprates. From our results we conclude that there is a single superconducting energy scale in the electron-doped cuprates.
Through variational Monte Carlo calculation on Gutzwiller projected wave functions, we study the quasiparticle(qp) weight for adding and removing an electron from a high temperature superconductor. We find the qp weight is particle-hole symmetric at sufficiently low energy. We propose to use the tunneling asymmetry as a tool to study the mechanism of electron incoherence in high temperature superconductors.
Neutron scattering experiments have played a crucial role in characterizing the spin and charge correlations in copper-oxide superconductors. While the data are often interpreted with respect to specific theories of the cuprates, an attempt is made here to distinguish those facts that can be extracted empirically, and the connections that can be made with minimal assumptions.
We present a theoretical framework for understanding the behavior of the normal and superconducting states of overdoped cuprate high temperature superconductors in the vicinity of the doping-tuned quantum superconductor-to-metal transition. The key ingredients on which we focus are d-wave pairing, a flat antinodal dispersion, and disorder. Even for homogeneous disorder, these lead to effectively granular superconducting correlations and a superconducting transition temperature determined in large part by the superfluid stiffness rather than the pairing scale.
We propose that an extension of the exciton concept to doped Mott insulators offers a fruitful insight into challenging issues of the copper oxide superconductors. In our extension, new fermionic excitations called cofermions emerge in conjunction to generalized excitons. The cofermions hybridize with conventional quasiparticles. Then a hybridization gap opens, and is identified as the pseudogap observed in the underdoped cuprates. The resultant Fermi-surface reconstruction naturally explains a number of unusual properties of the underdoped cuprates, such as the Fermi arc and/or pocket formati…
We calculate the Nernst signal in disordered conductors with the chemical potential near the mobility edge. The Nernst effect originates from interference of itinerant and localised-carrier contributions to the thermomagnetic transport. It reveals a strong temperature and magnetic field dependence, which describes quantitatively the anomalous Nernst signal in high-Tc cuprates.
Transport properties of high transition temperature (high-Tc) superconductors have been shown to have two distinct relaxation rates. We argue that this apparent inconsistence can be resolved with an effective carrier density n linear in temperature T. Experimental evidences both for and against this explanation are analyzed and we conclude that this offers a simple yet promising scenario. Above the pseudogap temperature T* the normal state of high-Tc cuprates is close to a Fermi liquid. It however assumes non-Fermi- liquid behaviors below T*.
We present a review of the vortex-Nernst effect in the 3 cuprate families La_{2-x}Sr_xCuO_4, Bi_2Sr_2CaCu_2O_8, and YBa_2Cu_3O_{y}, and discuss the scenario that the superconducting transition in the hole-doped cuprates corresponds to the destruction of long-range phase coherence rather than the vanishing of the order-parameter amplitude.
Normal state orbital diamagnetism of charged bosons quantitatively accounts for recent high-resolution magnetometery results near and above the resistive critical temperature Tc of superconducting cuprates. Our parameter-free descriptions of normal state diamagnetism, Tc, upper critical fields and specific heat anomalies unambiguously support the 3D Bose-Einstein condensation at Tc of preformed real-space pairs with zero off-diagonal order parameter above Tc, at variance with phase fluctuation (or vortex) scenarios of the "normal" state of cuprates.
The electronic structure of cuprate superconductors is studied within the kinetic energy driven superconducting mechanism in the presence of the out-of-plane impurities. With increasing the impurity concentration, although both superconducting coherence peaks around nodal and antinodal regions are suppressed, the position of the leading-edge mid-point of the electron spectrum around the nodal region remains at the same position, while it is shifted towards higher binding energies around the antinodal region, this leads to a strong deviation from the monotonic d-wave superconducting gap in the …
We describe a reversible, spatially-controlled doping method for cuprate films. The technique has been used to create superconductor-antiferromagnetic insulator-superconductor (S-AFI-S) junctions and optimally doped superconductor-underdoped superconductor-optimally doped superconductor (OS-US-OS) cuprate structures. We demonstrate how the S-AFI-S structure can be employed to reliably measure the transport properties of the antiferromagnetic insulator region at cryogenic temperatures using the superconductors as seamless electrical leads. We also discuss applied and fundamental issues which ma…
A d-wave superconductor, its phase coherence progressively destroyed by unbinding of vortex-antivortex pairs, suffers an instability related to chiral symmetry breaking in two-flavor QED$_3$. The chiral manifold exhibits large degeneracy spanned by physical states acting as inherent ``competitors'' of d-wave superconductivity. Two of these states are associated with antiferromagnetic insulator and ``stripe'' phases, known to be stable in the pseudogap regime of cuprates near half-filling. The theory also predicts additional, yet unobserved state: a d+ip phase-incoherent superconductor.
Charge and spin stripe order is a type of electronic crystal observed in certain layered cuprates associated with high-temperature superconductivity. Quantum-disordered stripes could be relevant for understanding the superconductivity. Here I discuss recent experimental characterizations of the stripe-ordered state in La(1.875)Ba(0.125)CuO(4), and compare them with properties of superconducting compositions.
Coexistence of antiferromagnetism and d-wave superconductivity within a CuO_2 plane was recently observed in a wide doping region for multilayer high-temperature cuprate superconductors. We find that the experimental phase diagram is well reproduced in the slave-boson mean-field scheme of the two-dimensional t-J model by including antiferromagnetic order. We argue that weak three dimensionality coming from a multilayer structure is sufficient to stabilize antiferromagnetic order and its coexistence with superconductivity.
We calculate scattering interference patterns for various electronic states proposed for the pseudogap regime of the cuprate superconductors. The scattering interference models all produce patterns whose wavelength changes as a function of energy, in contradiction to the energy-independent wavelength seen by scanning tunneling microscopy (STM) experiments in the pseudogap state. This suggests that the patterns seen in STM local density of states measurements are not due to scattering interference, but are rather the result of some form of ordering.
This paper summarizes experimental results presented at the international conference honoring Prof. C.N. Yang's 80th birthday. I show seven examples that illustrate how one can use angle-resolved photoemission spectroscopy to gain insights into the many-body physics responsible for the rich phase diagram of cuprate superconductors. I hope to give the reader a snapshot of the evolution of this experimental technique from a tool to study chemical bonds and band structure to an essential many-body spectroscopy for one of the most important physics problems of our time.
Recent experiments in underdoped hole-doped cuprates have shown the presence of two energy scales in the Raman spectrum in the superconducting state. This feature has a natural explanation in some models in which pseudogap and superconductivity compete. In electron-doped cuprates antiferromagnetic correlations are believed to survive in the superconducting state, and to produce a pseudogap above the critical temperature. Contrary to hole-doped systems, in electron-doped compounds only one energy scale appear since the pair breaking Raman intensity peaks in both B$_{1g}$ (antinodal) and B$_{2g}…
High Tc superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic X-ray scattering (RIXS) to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors [La2-xSrxCuO4 (LSCO) and Bi2Sr1.6La0.4CuO6+d (Bi2201)], crucially completing t…
We study the emergence of a magnetic resonance in the superconducting state of the electron-doped cuprate superconductors. We show that the recently observed resonance peak in the electron-doped superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-δ}$ is consistent with an overdamped spin exciton located near the particle-hole continuum. We present predictions for the magnetic-field dependence of the resonance mode as well as its temperature evolution in those parts of the phase diagram where $d_{x^2-y^2}$-wave superconductivity may coexist with an antiferromagnetic spin-density wave.
Following the identification of the pairing state, the major challenge in understanding the cuprate superconductors has been determining the evolution with doping and temperature of their anomalous normal state behavior. Key to this understanding is the experimentally determined magnetic phase diagram for the cuprates, which provides information on the protected magnetic properties of the normal state, generic behavior that is reliably the same one system to the next, regardless of details. I discuss the constraints this places on candidate quantum protectorates, and the status of microscopic …
Using as a model the Hubbard Hamiltonian we determine various basic properties of electron-doped cuprate superconductors like ${Nd}_{2-x}{Ce}_{x}{CuO}_{4}$ and ${Pr}_{2-x}{Ce}_{x}{CuO}_{4}$ for a spin-fluctuation-induced pairing mechanism. Most importantly we find a narrow range of superconductivity and like for hole-doped cuprates $d_{x^{2}-y^{2}}$ - symmetry for the superconducting order parameter. The superconducting transition temperatures $T_{c}(x)$ for various electron doping concentrations $x$ are calculated to be much smaller than for hole-doped cuprates due to the different Fermi surf…
In this paper, we review the low energy electronic structure of the kinetic energy driven d-wave cuprate superconductors. We give a general description of the charge-spin separation fermion-spin theory, where the constrained electron is decoupled as the gauge invariant dressed holon and spin. In particular, we show that under the decoupling scheme, the charge-spin separation fermion-spin representation is a natural representation of the constrained electron defined in a restricted Hilbert space without double electron occupancy. Based on the charge-spin separation fermion-spin theory, we have …
Recent experiments on Bi-based cuprate superconductors have revealed an unexpected enhancement of the pairing correlations near the interstitial oxygen dopant ions. Here we propose a possible mechanism -- based on local screening effects -- by which the oxygen dopants do modify the electronic parameters within the CuO_2 planes and strongly increase the superexchange coupling J. This enhances the spin pairing effects locally and may explain the observed spatial variations of the density of states and the pairing gap.
We report on semiclassical angle-dependent magnetoresistance oscillations (AMRO) and the Shubnikov-de Haas effect in the electron-overdoped cuprate superconductor Nd$_{2-x}$Ce$_x$CuO$_4$. Our data provide convincing evidence for magnetic breakdown in the system. This shows that a reconstructed multiply-connected Fermi surface persists, at least at strong magnetic fields, up to the highest doping level of the superconducting regime. Our results suggest an intimate relation between translational symmetry breaking and the superconducting pairing in the electron-doped cuprate superconductors.
A method is proposed to test for the nature of the pseudogap phase in cuprates using the recently developed technique of Fourier transform scanning tunneling spectroscopy. We show that the observed quasiparticle interference patterns depend critically on the quasiparticle coherence factors, making it possible to distinguish between the pseudogap dominated by superconducting fluctuations and by various particle-hole condensates.
Fluctuation effects in underdoped cuprates under high fields are examined by trying to fit theoretical results to resistivity and Nernst data in vortex states. The superconducting (SC) fluctuation in underdoped cuprates includes not only the ordinary thermal contribution but also a large amount of quantum dynamical contributions. Together with this, the presence of a SC pseudogap region T_0-T_{c0} increasing with underdoping is found to be the origin of the Nernst coefficient becoming anomalously smaller and the in-plane coherence length {\it apparently} increasing with underdoping.
Exciting new work on Bi2212 shows the presence of non-trivial spin-orbit coupling effects as seen in spin resolved ARPES data [Gotlieb et al., Science, 362, 1271-1275 (2018)]. Motivated by these observations we consider how the picture of spin-orbit coupling through local inversion symmetry breaking might be observed in cuprate superconductors. Furthermore, we examine two spin-orbit driven effects, the spin-Hall effect and the Edelstein effect, focusing on the details of their realizations within both the normal and superconducting states.
There is compelling evidence for a strong electron-phonon interaction (EPI) in cuprate superconductors from the isotope effects on the supercarrier mass, high resolution angle resolved photoemission spectroscopies (ARPES), a number of optical and neutron-scattering measurements in accordance with our prediction of high-temperature superconductivity in polaronic liquids. A number of observations point to the possibility that high-Tc cuprate superconductors may not be conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, but rather derive from the Bose-Einstein condensation (BEC) of real…
We report time-resolved measurements of the photoinduced change in reflectivity, Delta R, in the Bi2Sr2Ca(1-y)Dy(y)Cu2O(8+delta) (BSCCO) system of cuprate superconductors as a function of hole concentration. We find that the kinetics of quasiparticle decay and the sign of Delta R both change abruptly where the superconducting transition temperature Tc is maximal. These coincident changes suggest that a sharp transition in quasiparticle dynamics takes place precisely at optimal doping in the BSCCO system.
