Incommensurate Charge and Spin Fluctuations in d-wave Superconductors

TL;DR

This paper analytically investigates charge and spin fluctuations in d-wave superconductors, revealing incommensurate charge modes and conditions for magnetic peaks, with implications for understanding high-temperature superconductivity.

Contribution

It provides analytic results for charge and spin susceptibilities in d-wave superconductors, highlighting incommensurate charge modes and the conditions for magnetic peak formation.

Findings

Charge structure factor peaks form an ellipse around key wave vectors.

Strong interactions are needed for magnetic peaks near ${f Q}_{ ext{pi}}$.

Magnetic peaks occur near incommensurate wave vectors under certain conditions.

Abstract

We show analytic results for the irreducible charge and spin susceptibilities, $\chi_0 (\omega, {\bf Q})$, where ${\bf Q}$ is the momentum transfer between the nodes in d-wave superconductors. Using the BCS theory and a circular Fermi surface, we find that the singular behavior of the irreducible charge susceptibility leads to the dynamic incommensurate charge collective modes. The peaks in the charge structure factor occur at a set of wave vectors which form an ellipse around ${\bf Q}_{\pi}=(\pi,\pi)$ and ${\bf Q}_0=(0,0)$ in momentum space with momentum dependent spectral weight. It is also found that, due to the non-singular irreducible spin susceptibility, an extremely strong interaction via random phase approximation is required to support the magnetic peaks near ${\bf Q}_{\pi}$. Under certain conditions, the peaks in the magnetic structure factor occur near ${\bf Q}=(\pi,\pi (1 \pm \delta))$ and $(\pi (1 \pm \delta),\pi)$.