Comment on: Calculation of an Enhanced $A_{1g}$ Symmetry Mode Induced by Higgs Oscillations in the Raman Spectrum of High-Temperature Cuprate Superconductors

TL;DR

This paper critically examines a recent claim about Higgs mode enhancement in the Raman spectrum of cuprates, identifying errors that invalidate the original conclusion about the $A_{1g}$ symmetry mode.

Contribution

It provides a detailed critique of previous work, correcting the theoretical approach and clarifying the role of diagram counting in Raman response calculations.

Findings

Identification of overcounting in diagrammatic calculations

Invalidation of previous Higgs mode enhancement claims

Clarification of correct theoretical framework for Raman response

Abstract

In a recent manuscript Phys. Rev. Lett. 127, 197001 (2021) Puviani et al. claim that the Higgs mode gives an enhancement of the Raman response in the symmetric $A_{1g}$ Raman channel of cuprates. Here we report a series of technical mistakes in their derivation that completely invalidate this conclusion. In particular, the Raman response function contains two renormalized vertices, with a clearly overcounting of diagrams and uncontrolled results for the Higgs-mode contribution.