Imaging quasiparticle interference in Bi2Sr2CaCu2O8+delta

Scanning tunneling spectroscopy of the high-Tc superconductor Bi2Sr2CaCu2O8+delta reveals weak, incommensurate, spatial modulations in the tunneling conductance. Images of these energy-dependent modulations are Fourier analyzed to yield the dispersion of their wavevectors. Comparison of the dispersions with photoemission spectroscopy data indicates that quasiparticle interference, due to elastic scattering between characteristic regions of momentum-space, provides a consistent explanation for the conductance modulations, without appeal to another order parameter. These results refocus attention on quasiparticle scattering processes as potential explanations for other incommensurate phenomena in the cuprates. The momentum-resolved tunneling spectroscopy demonstrated here also provides a new technique with which to study quasiparticles in correlated materials.     

Temperature Dependence of the Superconducting Gap Anisotropy in Bi2Sr2CaCu2O8+x

Detailed data on the momentum-resolved temperature dependence of the superconducting gap of Bi(2)Sr(2)CaCu(2)O(8+x) are presented, complemented by similar data on the intensity of the photoemission superconducting condensate spectral area. The gap anisotropy between the Gamma-Mand Gamma-X directions increases markedly with increasing temperature, contrary to what happens for conventional anisotropic-gap superconductors, such as lead. Specifically, the size of the superconducting gap along the Gamma-X direction decreases to values indistinguishable from zero at temperatures for which the gap retains virtually full value along the Gamma-M direction. These data rule out the simplest type of d-wave order parameter.     

Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O(8+delta)

We report atomic-scale characterization of the pseudogap state in a high-Tc superconductor, Bi2Sr2CaCu2O(8+delta). The electronic states at low energies within the pseudogap exhibit spatial modulations having an energy-independent incommensurate periodicity. These patterns, which are oriented along the copper-oxygen bond directions, appear to be a consequence of an electronic ordering phenomenon, the observation of which correlates with the pseudogap in the density of electronic states. Our results provide a stringent test for various ordering scenarios in the cuprates, which have been central in the debate on the nature of the pseudogap and the complex electronic phase diagram of these compounds.     

Temperature-induced momentum-dependent spectral weight transfer in Bi2Sr2CaCu2O8+delta

Angle-resolved photoemission data from the cuprate superconductor Bi2Sr2CaCu2O8+delta above and below the superconducting transition temperature Tc reveal momentum-dependent changes that extend up to an energy of about 0.3 electron volt, or 40kTc (where k is the Boltzmann constant). The data suggest an anomalous transfer of spectral weight from one momentum to another, involving a sizable momentum transfer Q approximately (0.45pi, 0). The observed Q is intriguingly near the charge-order periodicity required if fluctuating charge stripes are present.     

Excitation Gap in the Normal State of Underdoped Bi2Sr2CaCu2O8+delta

Angle-resolved photoemission experiments reveal evidence of an energy gap in the normal state excitation spectrum of the cuprate superconductor Bi2Sr2CaCu2O8+delta. This gap exists only in underdoped samples and closes around the doping level at which the superconducting transition temperature Tc is a maximum. The momentum dependence and magnitude of the gap closely resemble those of the dx2-y2 gap observed in the superconducting state. This observation is consistent with results from several other experimental techniques, which also indicate the presence of a gap in the normal state. Some possible theoretical explanations for this effect are reviewed.     

Superconductivity-induced transfer of in-plane spectral weight in Bi2Sr2CaCu2O8+delta

Optical data are reported on a spectral weight transfer over a broad frequency range of Bi2Sr2CaCu2O8+delta, when this material became superconducting. Using spectroscopic ellipsometry, we observed the removal of a small amount of spectral weight in a broad frequency band from 10(4) cm(-1) to at least 2 x 10(4) cm(-1), due to the onset of superconductivity. We observed a blue shift of the ab-plane plasma frequency when the material became superconducting, indicating that the spectral weight was transferred to the infrared range. Our observations are in agreement with models in which superconductivity is accompanied by an increased charge carrier spectral weight. The measured spectral weight transfer is large enough to account for the condensation energy in these compounds.     

Signature of superfluid density in the single-particle excitation spectrum of Bi(2)Sr(2)CaCu(2)O(8+delta)

We report that the doping and temperature dependence of photoemission spectra near the Brillouin zone boundary of Bi(2)Sr(2)CaCu(2)O(8+delta)exhibit unexpected sensitivity to the superfluid density. In the superconducting state, the photoemission peak intensity as a function of doping scales with the superfluid density and the condensation energy. As a function of temperature, the peak intensity shows an abrupt behavior near the superconducting phase transition temperature where phase coherence sets in, rather than near the temperature where the gap opens. This anomalous manifestation of collective effects in single-particle spectroscopy raises important questions concerning the mechanism of high-temperature superconductivity.     

Atomic-Scale Sources and Mechanism of Nanoscale Electronic Disorder in Bi2Sr2CaCu2O8+delta

The randomness of dopant atom distributions in cuprate high-critical temperature superconductors has long been suspected to cause nanoscale electronic disorder. In the superconductor Bi2Sr2CaCu2O8+delta, we identified populations of atomic-scale impurity states whose spatial densities follow closely those of the oxygen dopant atoms. We found that the impurity-state locations are strongly correlated with all manifestations of the nanoscale electronic disorder. This disorder occurs via an unanticipated mechanism exhibiting high-energy spectral weight shifts, with associated strong superconducting coherence peak suppression but very weak scattering of low-energy quasi-particles.     

Electronic origin of the inhomogeneous pairing interaction in the high-Tc superconductor Bi2Sr2CaCu2O8+delta

Identifying the mechanism of superconductivity in the high-temperature cuprate superconductors is one of the major outstanding problems in physics. We report local measurements of the onset of superconducting pairing in the high-transition temperature (Tc) superconductor Bi2Sr2CaCu2O8+delta using a lattice-tracking spectroscopy technique with a scanning tunneling microscope. We can determine the temperature dependence of the pairing energy gaps, the electronic excitations in the absence of pairing, and the effect of the local coupling of electrons to bosonic excitations. Our measurements reveal that the strength of pairing is determined by the unusual electronic excitations of the normal state, suggesting that strong electron-electron interactions rather than low-energy (<0.1 volts) electron-boson interactions are responsible for superconductivity in the cuprates.     

A New High-Temperature Superconductor: Bi2Sr3-x Cax Cu2O8+y

A new superconductor that displays onset behavior near 120 K has been identified as Bi(2)Sr(3-x)Ca(x)Cu(2)O(8+y), with x ranging from about 0.4 to 0.9. Single crystal x-ray diffraction data were used to determine a pseudo-tetragonal structure based on an A-centered orthorhombic subcell with a = 5.399 A, b= 5.414A, and c = 30.904 A. The structure contains copper-oxygen sheets as in La(2)CuO(4) and YBa(2)Cu(3)O(7), but the copper-oxygen chains present in YBa(2)Cu(3)O(7) do not occur in Bi(2)Sr(3-x)Ca(x)Cu(2)O(8+y). The structure is made up of alternating double copper-oxygen sheets and double bismuth-oxygen sheets. There are Ca(2+) and Sr(2+) cations between the adjacent Cu-O sheets; Sr(2+) cations are also found between the Cu-O and Bi-O sheets. Electron microscopy studies show an incommensurate superstructure along the a axis that can be approximated by an increase of a factor of 5 over the subcell dimension. This superstructure is also observed by x-ray diffraction on single crystals, but twinning can make it appear that the superstructure is along both a and b axes. Flux exclusion begins in our samples at about 116 K and is very strong by 95 K. Electrical measurements on a single crystal of Bi(2)Sr(3-x)Ca(x)Cu(2)O(8+y) show a resistivity drop at about 116 K and apparent zero resistivity at 91 K.     

The Origin of the Superstructure in Bi2Sr2CaCu2O8+dgr as Revealed by Scanning Tunneling Microscopy

Real-space images with atomic resolution of the BiO plane of Bi(2)Sr(2)CaCu(2)O(8+delta) were obtained with a scanning tunneling microscope. Single-crystal samples were cleaved and imaged under ultrahigh vacuum conditions at room temperature. The images clearly show the one-dimensional incommensurate superstructure along the b-axis that is common to this phase. High-resolution images show the position of the Bi atoms, revealing the structural nature of the superlattice. A missing row of Bi atoms occurs either every nine or ten atomic sites in both (110) directions, accounting for the measured incommensurate periodicity of the superstructure. A model is proposed that includes missing rows of atoms, as well as displacements of the atomic positions along both the a- and c-axis directions.     

High Critical-Current Density in the Heavily Pb-Doped Bi2Sr2CaCu2O8+delta Superconductor: Generation of Efficient Pinning Centers

Critical-current density (Jc) is a parameter of primary importance for potential applications of high-temperature copper oxide superconductors. It is limited principally by the breakdown of zero-resistive current due to thermally activated flux flow at high temperatures and high magnetic fields. One promising method to overcome this limitation is to introduce efficient pinning centers into crystals that can suppress the flux flow. A marked increase in Jc was observed in Bi2Sr2CaCu2O8+delta (Bi-2212) single crystals doped with a large amount of Pb. By electron microscopy, characteristic microstructures were revealed that probably underlie the observed enhancement in Jc: thin (10 to 50 nanometers), platelike domains having a modulation-free structure appeared with spacings of 50 to 100 nanometers along the b axis.     

关于不定方程 5x(x+1 )(x+2 )(x+3 ) =6y(y+1 )(y+2 )(y+3 )

运用递归序列和平方剩余的方法,证明了不定方程5x(x+1)(x+2)(x+3)=6y(y+1)(y+2)(y+3)仅有正整数解(x,y)=(21,20).     

Simultaneous Observation of Columnar Defects and Magnetic Flux Lines in High-Temperature Bi2Sr2CaCu2O8 Superconductors

Columnar defects generated by heavy-ion irradiation are promising structures for pinning magnetic flux lines and enhancing critical currents in superconductors with high transition temperatures. An approach that combines chemical etching and magnetic decoration was used to highlight simultaneously the distributions of columnar defects and magnetic flux lines in Bi(2)Sr(2)CaCu(2)O(8) superconductors. Analyses of images of the columnar defects and flux-line positions provide insight into flux-line pinning by elucidating (i) the occupancy of columnar defects by flux lines, (ii) the nature of topological defects in the flux-line lattice, and (iii) the translational and orientational order in this lattice.     

不定方程x(x+1)(x+2)(x+3)=33y(y+1)(y+2)(y+3)的整数解的研究

主要运用Pell方程、递推序列、同余式及(非)平方剩余等一些初等的证明方法,对不定方程x(x+1)(x+2)(x+3)=33y(y+1)(y+2)(y+3)的解进行了研究.证明了该不定方程仅有1组正整数解(x,y)=(9,3).同时给出了不定方程(x~2+3x+1)~2-33y~2=-32的全部整数解.     

Structural and Electronic Role of Lead in (PbBi)2Sr2CaCu2O8 Superconductors by STM

The structural and electronic effects of lead substitution in the high-temperature superconducting materials Pb(x)Bi(2-x)Sr(2)CaCu(2)O(8) have been characterized by scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Large-area STM images of the Bi(Pb)-O layers show that lead substitution distorts and disorders the one-dimensional superlattice found in these materials. Atomic-resolution images indicate that extra oxygen atoms are present in the Bi(Pb)-O layers. STS data show that the electronic structure of the Bi(Pb)-O layers is insensitive to lead substitution within +/-0.5 electron volt of the Fermi level; however, a systematic decrease in the density of states is observed at approximately 1 electron volt above the Fermi level. Because the superconducting transition temperatures are independent of x(Pb) (x 相似文献   

Observation of d(x2-y2)-like superconducting gap in an electron-doped high-temperature superconductor

High-resolution angle-resolved photoemission spectroscopy of the electron-doped high-temperature superconductor Nd(2-x)Ce(x)CuO4 (x = 0.15, transition temperature T(c) = 22 K) has found the quasiparticle signature as well as the anisotropic d(x2-y2)-like superconducting gap. The spectral line shape at the superconducting state shows a strong anisotropic nature of the many-body interaction. The result suggests that the electron-hole symmetry is present in the high-temperature superconductors.     

关于不定方程z^2＋2（2xy）^2=（x^2-y^2＋2xy）^2

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椭圆曲线 y2 = (x +2 )( x2 -2x + p ) 的整数点

利用Legendre符号、同余式、Pell方程的解的性质等初等方法证明了:当p=36s~2-5(s∈Z+,2s),而6s~2-1,12s~2+1均为素数时,椭圆曲线y~2=(x+2)(x~2-2x+p)仅有整数点为(x,y)=(-2,0).     

已知条件概率P(x=t|x+y=t)求P(x=t)和P(y=t)的问题

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