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In the study of dynamic charge order correlations in the cuprates, most highenergy-resolution resonant inelastic x-ray scattering (RIXS) measurements havefocused on momenta along the high-symmetry directions of the copper oxideplane. However, electron scattering along other in-plane directions should notbe neglected as they may contain information relevant, for example, to theorigin of charge order correlations or to our understanding of the isotropicscattering responsible for strange metal behavior in cuprates. We reporthigh-resolution resonant inelastic x-ray scattering (RIXS) experiments thatreveal 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 phononline as a marker for the presence of charge-order-related dynamic electroncorrelations. The experiments show that these dynamic correlations exist atenergies below approximately $70$ meV and are centered around a quasi-circularmanifold in the $q_x$-$q_y$ scattering plane with radius equal to the magnitudeof the charge order wave vector, $q_{CO}$. We also demonstrate how thisphonon-tracking procedure provides the necessary experimental precision to ruleout 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 theobserved correlations.

science advances

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