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

Abstract

In the simplest model of magnetic pairing, the transition temperature to the superconducting state depends on the dynamical susceptibility $χ({\bf q},ω)$. We discuss how $T_c$ is affected by different momentum and frequency parts of $χ({\bf q},ω)$ for nearly antiferromagnetic and nearly ferromagnetic metals in two dimensions. While in the case of phonon-mediated superconductivity any addition of spectral weight to $α^2F(ω)$ at $ω>0$ 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 ${\bf q} \sim (π,π)$ 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.