Friedel oscillations as a probe of fermionic quasiparticles

Abstract

When immersed in a see of electrons, local impurities give rise to density modulations known as Friedel oscillations. In spite of the generality of this phenomenon, the exact shape of these modulations is usually computed only for non-interacting electrons with a quadratic dispersion relation. In actual materials, Friedel oscillations are a viable way to access the properties of electronic quasiparticles, including their dispersion relation, lifetime, and pairing. In this work we analyze the signatures of Friedel oscillations in STM and X-ray scattering experiments, focusing on the concrete example of cuprates superconductors. We identify signatures of Friedel oscillations seeded by impurities and vortexes, and explain experimental observations that have been previously attributed to a competing charge order. Contents

Holographic maps of quasiparticle interference

“…This peak is a distinctive property of local modulations of the chemical potential 30 and is absent (or very weak) in the experimental data of Fig. 2.…”

“…Following our earlier findings 29,30 we claim that the checkerboard-type short-range order observed in STM experiments simply corresponds to Friedel oscillations around local impurities, rather than to a competing charge-density-wave (CDW) order. We specifically consider the scattering of quasiparticles with finite lifetime from a local modulation of the pairing gap.…”

“…We find that h maps are invariant under ensemble average, up to an overall wavevectorindependent phase factor, e on the case of one dominant type of scatterers, relevant to superconducting cuprates 30,34 .…”

“…S2(a-d) we consider local modulations of the chemical potential, T k = σ z , where σ z is a Pauli matrix (see Methods section and Ref. [30] for details).…”

“…The resulting h maps deliver new information about properties of the quasiparticle scattering at the atomic level. These maps can be theoretically predicted by first computing the scattering amplitude from a one-band (or few-band) effective model, and then convoluting it with a trial Wannier function (see also The experimental measurement of h maps demonstrates that FT-STS maps of cuprates have a global s-wave rotational symmetry and are consistent with a model of Friedel oscillations around local impurities 29,30 . Because the only major assumption of our work is the validity of Bloch theorem for conduction-band electrons, we expect our approach to find important applications in the study of strongly correlated materials.…”