Low-energy quasi-circular electron correlations with charge order wavelength in $\textrm{Bi}_2\textrm{Sr}_2\textrm{Ca}\textrm{Cu}_2\textrm{O}_{8+\delta}$

TL;DR

This study uses high-resolution RIXS to reveal low-energy, quasi-circular electron correlations in underdoped Bi-2212 cuprates, centered around the charge order wave vector, providing new insights into charge order dynamics.

Contribution

It demonstrates the existence of isotropic, low-energy charge correlations in the scattering plane, extending understanding beyond high-symmetry directions in cuprates.

Findings

Dynamic correlations exist below 70 meV energy.

Correlations form a quasi-circular pattern in momentum space.

Short-range directional charge order fluctuations are ruled out as the cause.

Abstract

In the study of dynamic charge order correlations in the cuprates, most high energy-resolution resonant inelastic x-ray scattering (RIXS) measurements have focused on momenta along the high-symmetry directions of the copper oxide plane. However, electron scattering along other in-plane directions should not be neglected as they may contain information relevant, for example, to the origin of charge order correlations or to our understanding of the isotropic scattering responsible for strange metal behavior in cuprates. We report high-resolution resonant inelastic x-ray scattering (RIXS) experiments that reveal the presence of dynamic electron correlations over the $q_x$-$q_y$ scattering plane in underdoped $\textrm{Bi}_2\textrm{Sr}_2\textrm{Ca}\textrm{Cu}_2\textrm{O}_{8+\delta}$ with $T_c=54$ K. We use the softening of the RIXS-measured bond stretching phonon line as a marker for the presence of charge-order-related dynamic electron correlations. The experiments show that these dynamic correlations exist at energies below approximately $70$ meV and are centered around a quasi-circular manifold in the $q_x$-$q_y$ scattering plane with radius equal to the magnitude of the charge order wave vector, $q_{CO}$. We also demonstrate how this phonon-tracking procedure provides the necessary experimental precision to rule out fluctuations of short-range directional charge order (i.e. centered around $[q_x=\pm q_{CO}, q_y=0]$ and $[q_x=0, q_y=\pm q_{CO}]$) as the origin of the observed correlations.