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

TL;DR

This paper explains the sharp low energy feature in ARPES spectra of cuprate superconductors as a result of forward scattering impurities, linking it to the superconducting gap and providing insights into the fluctuation spectrum.

Contribution

The study offers a quantitative analysis using Eliashberg equations to connect the low energy feature with forward scattering impurities in cuprates, clarifying its origin.

Findings

The low energy feature (LEF) arises from forward scattering impurities.

LEF energy increases proportionally with $T_c$ below $T_c$.

The impurity scattering rate is modified by the superconducting gap.

Abstract

There is an enormous interest in renormalization of quasi-particle (qp) dispersion relation of cuprate superconductors both below and above the critical temperature $T_c$ because it enables determination of the fluctuation spectrum to which the qps 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$_{8+\delta}$ (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.