Temperature Dependence of the Momentum-Resolved Static Spin Susceptibility in a Mott-Proximate Cuprate Model

TL;DR

The paper investigates how the static, momentum-resolved spin susceptibility in a Mott-proximate cuprate model evolves with temperature, focusing on the antinodal pseudogap regime at $oldsymbol{q}=(\pi,\pi)$ and $(\pi,0)$. By combining Lindhard (bare) and dressed-bubble formalisms with RPA analysis and CDMFT-derived self-energies, the authors show that the onset of thermally activated spin response occurs near the superconducting $T_c$ and that approaching the antinodal van Hove region markedly enhances axial particle–hole excitations. The results indicate a correlation between cuprate superconductivity and suppression of low-energy antinodal spin fluctuations, with the pseudogap reducing low-$\omega$ phase space and potentially mitigating spin-fluctuation–mediated dephasing of $d$-wave pairing. Overall, the work links the pseudogap, van Hove physics, and spin susceptibility to the emergence of superconductivity in HTSC cuprates, offering a framework to interpret temperature-dependent spin dynamics in these materials.

Abstract

This paper presents the temperature dependence of the static spin susceptibility at $\mathbf{q} = (π, π)$ and $\mathbf{q} = (π, 0)$ in a Mott-proximate cuprate model with an antinodal pseudogap -- a model system for high-temperature superconducting (HTSC) cuprates. The results show the susceptibility onset temperature tracks the critical temperature ($T_c$) of HTSCs with a comparable scale across the electron filling factor. Also, as the electron filling decreases and the chemical potential approaches the antinodal van Hove region, the susceptibility at $\mathbf{q}=(π,0)$ -- the axial particle-hole response -- grows markedly. It suggests that the emergence of cuprate superconductivity correlates with a suppression of low-energy antinodal spin response and associated particle-hole excitations, which would otherwise dephase $d$-wave pairing, commonly attributed to spin fluctuations. In this context, the pseudogap partially suppresses antinodal spectral weight near $ω= 0$, thereby reducing the low-$ω$ particle-hole phase space.

Figures (11)

• Figure 1: Temperature dependence of $\chi(\mathbf{q}=0;T)$ at $\Delta=0$, evaluated using the Lindhard (bare) (blue and flatter curve) and the dressed-bubble susceptibility (orange). The chemical potentials are $\mu(4\mathrm{K})=-0.26~\mathrm{eV}$ and $1.21~\mathrm{eV}$, corresponding to $n=1.0$ (metallic case).
• Figure 2: Temperature dependence of the Lindhard susceptibility $\chi(\mathbf{q},T)$ at $\mathbf{q}=(\pi, \pi)$ for several gap values $\Delta (\mathrm{eV})$ and corresponding $\mu(4\mathrm{K}) (\mathrm{eV})$. From bottom to top: $n = 0.75, 0.80, 0.85, 0.90,$ and $0.95$.
• Figure 3: Temperature dependence of the Lindhard susceptibility $\chi(\mathbf{q},T)$ at $\mathbf{q}=(\pi,0)$ for several several gap values $\Delta (\mathrm{eV})$ and corresponding $\mu(4\mathrm{K}) (\mathrm{eV})$. From top to bottom: $n = 0.75, 0.80, 0.85, 0.90,$ and $0.95$.
• Figure 4: Temperature dependence of the dressed-bubble susceptibility $\chi(\mathbf{q}, T)$ at $\mathbf{q}=(\pi,\pi)$ for several gap values $\Delta (\mathrm{eV})$ and corresponding $\mu_{\mathrm{}} (4\mathrm{K}) (\mathrm{eV})$. From top to bottom at 150K: $n = 0.80, 0.85, 0.60, 0.90,$ and $0.95$.
• Figure 5: Temperature dependence of the dressed-bubble susceptibility $\chi(\mathbf{q}, T)$ at $\mathbf{q}=(\pi,0)$ for several gap values $\Delta (\mathrm{eV})$ and corresponding $\mu_{\mathrm{}}(4\mathrm{K}) (\mathrm{eV})$ (Enlarged view of Fig. \ref{['fig:arrhenius_bubble_06_pizero']}). From top to bottom at 150K: $n = 0.85, 0.80, 0.90,$ and $0.95$.