Sharp low-energy feature in single-particle spectra due to forward scattering in d-wave cuprate superconductors

There is an enormous interest in the renormalization of the quasiparticle (qp) dispersion relation of cuprate superconductors both below and above the critical temperature T_{c} because it enables the determination of the fluctuation spectrum to which the qp's are coupled. A remarkable discovery by angle-resolved photoemission spectroscopy (ARPES) is a sharp low-energy feature (LEF) in qp spectra well below the superconducting energy gap but with its energy increasing in proportion to T_{c} and its intensity increasing sharply below T_{c}. This unexpected feature needs to be reconciled with d-wave superconductivity. Here, we present a quantitative analysis of ARPES data from Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} (Bi2212) using Eliashberg equations to show that the qp scattering rate due to the forward scattering impurities far from the Cu-O planes is modified by the energy gap below T_{c} and shows up as the LEF. This is also a necessary step to analyze ARPES data to reveal the spectrum of fluctuations promoting superconductivity.