Can the bosonic coupling constant be extracted from the ARPES scattering rate in cuprate superconductors?

TL;DR

This paper critically examines the methods used to extract bosonic coupling constants from ARPES data in cuprate superconductors, highlighting inconsistencies and ambiguities that challenge the interpretation of the pairing mechanism.

Contribution

It analyzes the validity of the 'Fermi-Bose' division procedure in ARPES data and discusses implications for the applicability of Eliashberg theory in cuprates.

Findings

The bosonic coupling constant from ARPES line-width is very small (<0.2).

The coupling constant from the nodal kink is much larger.

The 'Fermi-Bose' division procedure is ambiguous and questionable.

Abstract

The recent ARPES results for the imaginary part of the self-energy obtained on a number of HTSC bismuthates \cite{Kordyuk} are analyzed. By accepting the ''Fermi-Bose'' {\it division-procedure} of the self-energy into the Fermi-liquid and bosonic parts - which is proposed in \cite{Kordyuk}, one obtains very small bosonic coupling constant $\lambda_{B, Im} <0.2$. If this procedure would be correct then the standard Eliashberg theory makes any bosonic mechanism of pairing irrelevant. As a consequence we are confronted with a trilemma: (1) to abandon the ``Fermi-Bose'' division-procedure \cite{Kordyuk}; (2) to abandon the Eliashberg theory; (3) to abandon the interpretation of ARPES data within the three-step model, where the ARPES intensity is proportional to the quasiparticle spectral function $A(\mathbf{k},\omega)$. However, since the bosonic coupling constant extracted from the ARPES nodal kink at 70 meV \cite{Lanzara}, which measures the real part of the self-energy is much larger than the one extracted from the ARPES line-width this means that the ``Fermi-Bose'' division procedure done in \cite{Kordyuk} is ambiguous.