Power spectrum of many impurities in ad-wave superconductor

Abstract

Recently the structure of the measured local density of states power spectrum of a small area of the Bi2Sr2CaCu2O8 (BSCCO) surface has been interpreted in terms of peaks at an "octet" of scattering wave vectors determined assuming weak, noninterfering scattering centers. Using analytical arguments and numerical solutions of the Bogoliubov-de Gennes equations, we discuss how the interference between many impurities in a d-wave superconductor alters this scenario. We propose that the peaks observed in the power spectrum are not the features identified in the simpler analyses, but rather "background" structures which disperse along with the octet vectors. We further consider how our results constrain the form of the actual disorder potential found in this material.In the past few years, high-resolution scanning tunneling microscopy (STM) experiments on the cuprate superconductor BSCCO [1, 2,3,4,5,6,7,8,9,10,11] have obtained local information on electronic structure for the first time. The first great success of this technique was the observation of resonant defect states at low temperatures in the superconducting state [1, 2,3], confirming early proposals that such states should be reflected in the local density of states (LDOS) of dwave superconductors [12,13]. Subsequent experiments revealed the existence of nanoscale inhomogeneities [4,5,6,7] which are currently the subject of debate, being attributed either to interaction-driven effects such as stripe-formation [8,9] or to Friedel oscillations of weaklyinteracting quasiparticles [5,6]. At the heart of this debate lies the important question of whether, and if so in what ranges of doping, conventional BCS-like theories describe the ground state and low energy excitations of BSCCO. Recently it has been pointed out that, in inhomogeneous systems, the Fourier transform of the LDOS (FTDOS) contains information not only about the disorder potential, but about the kinematics of the associated pure system. That this must be so at some level is clear from the original one-impurity problem solved by Friedel[14]: a charge inserted in an electron gas gives rise to LDOS oscillations which vary at large distances as ∼ cos 2k F r/r 3 , so the wavelength of the LDOS "ripples" caused by a single impurity gives the Fermi wave vector directly. A somewhat more sophisticated version of this argument, [10,15,16,17,18] still assuming scattering from a single or few impurities and noninteracting quasiparticles, suggested that the peaks in the FTDOS are due to scattering of quasiparticles by a weak disorder potential. In this case favored momentum transfers correspond to vectors q connecting two tips of quasiparticle constant energy contours which maximize the joint density of states (JDOS). This interpretation has been applied to recent experiments[11] which claim to map out a Fermi surface in agreement with angle-resolved photoemission (ARPES). In contrast to this, Howald et al. [8,9] identify nondispersing features in the FTDOS from their experiments, which they suggest are indicat...

Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

“…Calculations of QPI from single site and multiple impurities 29,32,[42][43][44] reproduce the locations of experimentally measured wavevectors, but the features in the QPI pattern are "streak-like" rather than "point-like" as in experiment. Zhu et.al 45 studied QPI from multiple impurities, and highlighted the need for more realistic impurity models. Other works have shown that many of the discrepancies between theory and experiment can be resolved by considering an extended long range impurity model, 46 or by including a spatially inhomogeneous chemical potential and superconducting gap.…”

Universal disorder in Bi2Sr2CaCu2OAlldredge1, Fujita2, Eisaki3 et al. 2013Phys. Rev. B

“…This Tripartite structure defines three different regions that are each associated with three different q -space excitations, examples of which are shown in figure 2. In red at low energies is the dispersive QPI, which are excitations from the superconducting ground state likely caused by weak scattering 5,10,32 . Above these states in energy is the non-dispersive q 1 * modulation whose -3 dB intensity corresponds to the end of the kink in the mean LDOS(E) 11 .…”

Defect and anisotropic gap-induced quasi-one-dimensional modulation of the local density of states ofYBa2Cu3Voo1, Chen2, Wu3 2003Phys. Rev. B

“…Very recently Anderson and Hedegård [17] also study the quantum interference between multiple impurities for a d x 2 −y 2 -wave superconductor, whose pairing state could become d x 2 −y 2 + id xy or d x 2 −y 2 + is-wave at some doping level. Our dilute multi-impurity regime discussed above is fundamentally different from that any one else [15][16][17] has studied. Let the length scale between the impurities be d 0 , and the distance away from the impurities, where we are interested, be d. Our interesting regime is then d 0 ∼ d > ∼ 20a (see Fig.…”

“…The case of multiple impurities for BSCCO is recently considered by Morr et al [15] and Zhu et al [16]. Very recently Anderson and Hedegård [17] also study the quantum interference between multiple impurities for a d x 2 −y 2 -wave superconductor, whose pairing state could become d x 2 −y 2 + id xy or d x 2 −y 2 + is-wave at some doping level.…”