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...

We investigate the effect of elastic forward scattering on the ARPES spectrum of the cuprate superconductors. In the normal state, small angle scattering from out-of-plane impurities is thought to broaden the ARPES spectral response with minimal effect on the resistivity or the superconducting transition temperature Tc. Here we explore how such forward scattering affects the ARPES spectrum in the d-wave superconducting state. Away from the nodal direction, the one-electron impurity scattering rate is found to be suppressed as ω approaches the gap edge by a cancellation between normal and anomalous scattering processes, leading to a square-root-like feature in the spectral weight as ω approaches −∆ k from below. For momenta away from the Fermi surface, our analysis suggests that a dirty optimally or overdoped system will still display a sharp but nondispersive peak which could be confused with a quasiparticle spectral feature. Only in cleaner samples should the true dispersing quasiparticle peak become visible. At the nodal point on the Fermi surface, the contribution of the anomalous scattering vanishes and the spectral weight exhibits a Lorentzian quasiparticle peak in both energy and momentum. Our analysis, including a treatment of unitary scatterers and inelastic spin fluctuation scattering, suggests explanations for the sometimes mysterious lineshapes and temperature dependences of the peak structures observed in the Bi2Sr2CaCu2O8 system.

Due to an overall sign error of the right-hand side of Eq. ͑6͒ of Ref. 1, the approximate form of the gap renormalization due to forward impurity scattering in Eqs. ͑13͒ and ͑14͒ was incorrect, along with Figs. 2 and 3. The corrected figures are given here as Figs. 2 and 3. Note that in the forward scattering limit → 0 the effective gap slope increases.All other results in Ref. 1 shown in subsequent figures were obtained with the correct minus sign in Eq. ͑6͒. Equation ͑19͒, however, is incorrect because it was derived using the incorrect forward scattering limit for ṽ 2 / v 2 . The correct result as → 0 is that ṽ 2 diverges as ṽ 2 / v 2 ϰ −2/3 , and a transparent analytical result for ⌫ el ͑T͒ in the dirty limit ͓Eq. ͑19͔͒ is not obtained.In an unrelated minor error, Eq. ͑16͒ is missing a factor of 2; it should read ⌫ el ͑T͒Ӎ2ṽ 2 exp͑−ṽ 2 / ⌫ 0 ͒. All other equations are unaffected, and the conclusions of the paper do not change. Phys. Rev. B 72, 214512 ͑2005͒. 0 0.2 0.4 0.6 0.8 1 Κ 1 2 3 4 5 v 2 v 2 0 v 2 0.5 0 v 2 0.25 0 v 2 0.1 FIG. 2. Gap slope renormalization ṽ 2 / v 2 vs inverse scattering range from the solution of Eqs. ͑12͒ and ͑14͒ of Ref. 1. 0 0.5 1 T T c 0 0.1 0.2 0.3 el 0 a 2 1.5 1 0.5 0 Ω 0 0 0.1 0.2 0.3 0.4 el 0 b 0 0.5 1 T T c 0 0.2 0.4 0.6 el 0 c 2 1.5 1 0.5 0 Ω 0 0 0.2 0.4 0.6 0.8 el 0 d Κ 0.5 Κ 1.0 Κ 2.0 FIG. 3. Evaluation of the elastic nodal scattering rate ⌫ el from Eqs. ͑12͒ and ͑14͒ of Ref. 1.͑a͒ Temperature dependence of ⌫ el ͑ =0,T͒ for three values of the impurity potential range parameter = 0.5, 1.0, and 2.0 with ⌫ 0 = 0.5⌬ 0 ; ͑b͒ energy dependence of ⌫ el ͑ , T =0͒ for the same parameters; ͑c͒, ͑d͒ same as ͑a͒, ͑b͒ but for ⌫ 0 = 0.25⌬ 0 .

Recent experiments introducing controlled disorder into optimally doped cuprate superconductors by both electron irradiation and chemical substitution have found unusual behavior in the rate of suppression of the critical temperature Tc vs. increase in residual resistivity. We show here that the unexpected discovery that the rate of Tc suppression vs. resistivity is stronger for out-of-plane than for in-plane impurities may be explained by consistent calculation of both Tc and resistivity if the potential scattering is assumed to be nearly forward in nature. For realistic models of impurity potentials, we further show that significant deviations from the universal Abrikosov-Gor'kov Tc suppression behavior may be expected for out of plane impurities.PACS numbers: 74.25.Jb, 74.20.Fg The destruction of superconductivity by disorder has been traditionally used to probe the nature of the superconducting state. In classic superconductors, pairbreaking is caused only by magnetic impurities 1 , and the functional form of the T c suppression, when plotted vs. impurity concentration or change in normal state resistivity, is known to follow the universal curve predicted by Abrikosov and Gor'kov (AG) 2 . In unconventional superconductors, ordinary nonmagnetic impurities are also expected to break pairs, and in the simplest approximation where the impurities are treated as point-like (deltafunction) potential scatterers, the T c suppression also follows the AG form.As in so many other respects, the experimental situation in the cuprates agrees qualitatively with the simplest notions of what should happen to d-wave superconductors in the presence of disorder, but differs in some important details. For example, when Zn is substituted for Cu in the Cu-O planes, T c is suppressed rapidly as expected for a d-wave superconductor. Here, "rapidly" means that the disorder-induced scattering rate required to destroy superconductivity is on the order of the gap scale rather than the Fermi energy E F , as would be expected in an swave system. Nevertheless, the initial slope of the T c vs. ∆ρ curve found in experiment is a factor of 2-3 smaller than the universal AG curve 3 . This discrepancy has been attributed to scattering in higher angular momentum channels by several authors, who modelled the scattering potential with a separable form describing scattering in both s-and a single higher ℓ-wave channel 4,5 . This is a simple and tractable way of including the finite range of the scatterers qualitatively, but is neither consistent by the microscopics of screened impurities in the cuprates, nor capable of treating the limit of extreme forward scattering, claimed to be of relevance in the cuprate case 6,7,8 . Furthermore, in these studies T c is calculated as a function of the single-particle normal state scattering rate 1/τ N , as opposed to the transport rate 1/τ tr relevant for comparison to resistivity measurements.A further paradox was reported recently by Fujita et al. 13 , who showed that the rate of suppression dT c /dρ is s...

A new generation of angular-resolved photoemission spectroscopy (ARPES) measurements on the cuprate superconductors offer the promise of enhanced momentum and energy resolution. In particular, the energy and temperature dependence of the on-shell nodal (kx = ky) quasiparticle scattering rate can be studied. In the superconducting state, low temperature transport measurements suggest that one can describe nodal quasiparticles within the framework of a BCS d-wave model by including forward elastic scattering and spin-fluctuation inelastic scattering. Here, using this model, we calculate the temperature and frequency dependence of the on-shell nodal quasiparticle scattering rate in the superconducting state which determines the momentum width of the ARPES momentum distribution curves. For a zero-energy quasiparticle at the nodal momentum kN , both the elastic and inelastic scattering rate show a sudden decrease as the temperature drops below Tc, reflecting the onset of the gap amplitude. At low temperatures the scattering rate decreases as T 3 and approaches a zero temperature value determined by the elastic impurity scattering. For T > Tc, we find a quasilinear dependence on T . At low reduced temperatures, the elastic scattering rate for the nodal quasiparticles exhibits a quasilinear increase at low energy ω which arises from elastic scattering processes. The inelastic spin-fluctuation scattering leads to a low energy ω 3 dependence which, for ω 3∆0, crosses over to a quasilinear behavior.