Local quasiparticle lifetimes in ad-wave superconductor

Abstract

Scanning tunnelling spectroscopy (STS) measurements find that the surface of Bi-2212 is characterized by nanoscale sized regions, "gap patches," which have different magnitudes for the d-wave energy gap ∆0(r). Recent studies have shown that the tunnelling conductance can be fit using a BCS-type density of states for a d-wave superconductor with a local quasiparticle scattering rate. The fit is made with a scattering rate which varies linearly with energy and has a slope α(r) that is positively correlated with the local value of the gap. We consider first the question of what is actually measured in such an experiment. To this end we revisit a model of quasiparticle scattering by impurities and spin fluctuations which was previously used to describe the lifetimes of nodal quasiparticles measured by angle-resolved photoemission (ARPES). We argue that the broadening of the local density of states is determined, except in the case of localized impurity bound states, by the imaginary part of the self-energy of the system averaged over a small region. The size of this region is set by a mean free path which depends upon the energy. At low energies, this region is found to be significantly larger than a gap "patch", so that the density of states measured by STS is homogeneous in this energy range. At higher energies where the mean free path is comparable with the patch size, the density of states is inhomogeneous. We show that a local self-energy in the impurity-plus-spin fluctuation model, while not strictly linear, yields a local density of states (LDOS) nearly identical to the full theory, and argue that it is consistent with the STS data as well as the phenomenological linear scattering rate extracted from experiment. We also explore the qualitative consequences of this phenomenology for the spectral widths observed in ARPES and predict the existence of Fermi arcs in the superconducting state.

On the multi‐orbital band structure and itinerant magnetism of iron‐based superconductors

“…Models for spin fluctuations are based on the weak-coupling, itinerant limit, with superconductivity related to the presence of strong nesting between hole and electron sheets of the paramagnetic Fermi surface, which is also held responsible for the instability towards magnetism [42,43,48]. This possibility has been investigated using more ore less sound models of the band structure, combined with different many-body methods (RPA, FLEX, frG, model ME calculations) which do seem to agree on a picture with competing instabilities towards magnetism and superconductivity [42,43,[49][50][51][52][53][54][55][56][57][58][59][60]. The superconducting phase should be characterized by multiple gaps, with s and d symmetries almost degenerate.…”

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

“…In order to model the suppression of the gap peak without the filling in of the gap, a linear in energy lifetime term was used. This term is modeled on Born scattering in a weakly coupled d-wave BCS superconductor 20 , but the actual cause is most likely due to impurity-plus-spin fluctuations 21 . In the Tripartite model we find that both these lifetime terms are needed to match the LDOS(E).…”

Out-of-plane impurities induce deviations from the monotonicd-wave superconducting gap of cuprate superconductors

“…In this sense, the calculations in this kinetic energy driven superconductivity scheme are controllable without using any adjustable parameters. We emphasize that the Green's function (3) is obtained within the kinetic energy driven superconducting mechanism, although the similar phenomenological expression has been used to discuss the impurity effect in cuprate superconductors 24,25 . With the charge carrier BCS formalism (3) under the kinetic energy driven superconducting mechanism, we can now introduce the effect of impurity scatterers into the electronic structure.…”

“…Although this out-of-plane impurity effect in cuprate superconductors can also be discussed starting directly from a phenomenological d-wave BCS formalism 25,27 , in this paper we are primarily interested in exploring the general notion of the effects of the out-of-plane impurity scatterers in the kinetic energy driven cuprate superconductors in the superconducting state. The qualitative agreement between the present theoretical results and ARPES experimental data also indicates that the presence of the out-of-plane impurities has a crucial impact on the electronic structure of cuprate superconductors.…”