Elastic forward scattering in the cuprate superconducting state

TL;DR

This paper studies how elastic forward scattering affects ARPES spectra in cuprate superconductors, revealing unique spectral features and clarifying the nature of quasiparticle peaks in the superconducting state.

Contribution

It provides a detailed analysis of forward scattering effects on ARPES spectra in d-wave superconductors, including impurity and inelastic scattering, highlighting conditions for observing true quasiparticle peaks.

Findings

Suppression of impurity scattering rate near the gap edge

Presence of sharp nondispersive peaks in dirty samples

Lorentzian quasiparticle peaks at the nodal point

Abstract

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 $T_c$. 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 $\omega$ 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 $\omega$ approaches $-\Delta_\k$ 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 \BSCCO system.