Local quasiparticle lifetimes in a d-wave superconductor
S. Graser, P. J. Hirschfeld, D. J. Scalapino
DOI 10.1103/PhysRevB.77.184504 · Physical Review B
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Abstract
Scanning tunneling 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 Δ0(r). Recent studies have shown that the tunneling conductance can be fitted 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 photoelectron spectroscopy (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 on 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 nearly identical to the full theory, and we 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.
Source-reported materials — not catalogue approval
| Formula | Reported Tc (K) | Pressure (GPa) | Type |
|---|---|---|---|
| Bi2Sr2CaCu2O8 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula. | — | Pressure not reported | unknown |
| YBa2Cu3O7 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula. | — | Pressure not reported | unknown |
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