Screening in (d+s)-wave superconductors: Application to Raman scattering

We study the polarization-dependent electronic Raman response of untwinned YBa$_2$Cu$_3$O$_{7-\delta}$ superconductors employing a tight-binding band structure with anisotropic hopping matrix parameters and a superconducting gap with a mixing of $d$- and s-wave symmetry. Using general arguments we find screening terms in the B^{\}_{1g} scattering channel which are required by gauge invariance. As a result, we obtain a small but measurable softening of the pair-breaking peak, whose position has been attributed for a long time to twice the superconducting gap maximum. Furthermore, we predict superconductivity-induced changes in the phonon line shapes that could provide a way to detect the isotropic s-wave admixture to the superconducting gap.Comment: typos corrected, 6 pages, 3 figure

Influence of higher d-wave gap harmonics on the dynamical magnetic susceptibility of high-temperature superconductors

Using a fermiology approach to the computation of the magnetic susceptibility measured by neutron scattering in hole-doped high-Tc superconductors, we estimate the effects on the incommensurate peaks caused by higher d-wave harmonics of the superconducting order parameter induced by underdoping. The input parameters for the Fermi surface and d-wave gap are taken directly from angle resolved photoemission (ARPES) experiments on Bi{2}Sr{2}CaCu{2}O{8+x} (Bi2212). We find that higher d-wave harmonics lower the momentum dependent spin gap at the incommensurate peaks as measured by the lowest spectral edge of the imaginary part in the frequency dependence of the magnetic susceptibility of Bi2212. This effect is robust whenever the fermiology approach captures the physics of high-Tc superconductors. At energies above the resonance we observe diagonal incommensurate peaks. We show that the crossover from parallel incommensuration below the resonance energy to diagonal incommensuration above it is connected to the values and the degeneracies of the minima of the 2-particle energy continuum.Comment: 13 pages, 7 figure

Random Dirac Fermions and Non-Hermitian Quantum Mechanics

We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian operator can be obtained as the solution to a two-dimensional Dirac equation in the presence of a random gauge field. Consequences for the localization properties and the critical nature of the states are discussed.Comment: 5 pages, Latex, 1 figure, version published in PR

Gaussian field theories, random Cantor sets and multifractality

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.Comment: Extensive modifications of previous version; exact results replace numerical calculation

Two-photon fluorescence isotropic-single-objective microscopy

International audienceTwo-photon excitation provides efficient optical sectioning in three-dimensional fluorescence microscopy, independently of a confocal detection. In two-photon laser-scanning microscopy, the image resolution is governed by the volume of the excitation light spot, which is obtained by focusing the incident laser beam through the objective lens of the microscope. The light spot being strongly elongated along the optical axis, the axial resolution is much lower than the transverse one. In this Letter we show that it is possible to strongly reduce the axial size of the excitation spot by shaping the incident beam and using a mirror in place of a standard glass slide to support the sample. Provided that the contribution of sidelobes can be removed through deconvolution procedures, this approach should allow us to achieve similar axial and lateral resolution

Zero-modes in the random hopping model

If the number of lattice sites is odd, a quantum particle hopping on a bipartite lattice with random hopping between the two sublattices only is guaranteed to have an eigenstate at zero energy. We show that the localization length of this eigenstate depends strongly on the boundaries of the lattice, and can take values anywhere between the mean free path and infinity. The same dependence on boundary conditions is seen in the conductance of such a lattice if it is connected to electron reservoirs via narrow leads. For any nonzero energy, the dependence on boundary conditions is removed for sufficiently large system sizes.Comment: 12 pages, 11 figure

Isotropic Single Objective (ISO) microscopy : Theory and Experiment

International audienceIsotropic single-objective (ISO) microscopy is a recently proposed imaging technique that can theoretically exhibit the same axial and transverse resolutions as 4Pi microscopy while using a classical single-objective confocal microscope. This achievement is obtained by placing the sample on a mirror and shaping the illumination beam so that the interference of the incident and mirror-reflected fields yields a quasi-spherical spot. In this work, we model the image formation in the ISO fluorescence microscope and simulate its point spread function. Then, we describe the experimental implementation and discuss its practical difficulties