Sensitivity of the Superconducting Transition Temperature to Changes in the Spin-Fluctuation Spectral Weight

TL;DR

This paper investigates how the superconducting transition temperature ($T_c$) is influenced by changes in the spin-fluctuation spectral weight, revealing that magnetic spectral weight at certain momenta and low frequencies suppresses $T_c$ in nearly magnetic metals.

Contribution

It demonstrates that magnetic spectral weight at specific momenta and low frequencies reduces $T_c$, contrasting with phonon-mediated superconductivity where added spectral weight increases $T_c$.

Findings

Adding spectral weight at high frequencies increases $T_c$ in phonon-mediated superconductors.

Magnetic spectral weight at low frequencies and certain momenta suppresses $T_c$ in nearly magnetic metals.

Optimal frequency and momentum ranges for suppressing $T_c$ are identified for different magnetic tendencies.

Abstract

In the simplest model of magnetic pairing, the transition temperature to the superconducting state depends on the dynamical susceptibility $\chi({\bf q},\omega)$. We discuss how $T_c$ is affected by different momentum and frequency parts of $\chi({\bf q},\omega)$ for nearly antiferromagnetic and nearly ferromagnetic metals in two dimensions. While in the case of phonon-mediated superconductivity any addition of spectral weight to $\alpha^2F(\omega)$ at $\omega >0$ leads to an increase in $T_c$, we find that adding magnetic spectral weight at any momentum ${\bf q}$ and low frequencies ($[0:3T_c]$ and $[0:(5-9)T_c]$ for nearly antiferromagnetic and ferromagnetic metals respectively) leads to a suppression of $T_c$. The most effective frequency and momentum range consists of large momenta ${\bf q} \sim (\pi,\pi)$ and frequencies around $10T_c$ for nearly antiferromagnetic metals and small momenta ${\bf q} \sim 0$ and frequencies of approximately $(13-22)T_c$ for nearly ferromagnetic metals.