Dependence of $T_c$ on the $q-\omega$ structure of the spin-fluctuation spectrum

TL;DR

This paper investigates how the momentum and energy structure of spin fluctuations in YBCO$_{6.6}$ influence its superconducting transition temperature $T_c$, using a phenomenological analysis based on neutron scattering and ARPES data.

Contribution

It introduces a method to relate the $T_c$ variation to the functional derivative of the gap eigenvalue with respect to the spin susceptibility spectrum.

Findings

Different regions of the $q$ and $$ spectrum contribute variably to $T_c$.

The analysis highlights the importance of specific spin-fluctuation features near $T_c$.

The approach links experimental data to theoretical understanding of pairing mechanisms.

Abstract

A phenomenological spin-fluctuation analysis (Ref. 1), based upon inelastic neutron scattering (INS) and angular resolved photoemission spectroscopy (ARPES) data for ${\rm YBCO}_{6.6}(T_c=61K)$, is used to calculate the functional derivative of the d-wave eigenvalue $\lambda_d$ of the linearized gap equation with respect to the imaginary part of the spin susceptibility $\chi''(q,\omega)$ at 70K. For temperatures near $T_c$, the variation of $T_c$ with respect to $\chi''(q,\omega)$ is proportional to this functional derivative. Based on this, we discuss how different parts of the $q$ and $\omega$ dependent spin-fluctuation spectrum of YBCO$_{6.6}$ contribute to $T_c$.