Low-energy quasi-circular electron correlations with charge order wavelength in Bi₂Sr₂CaCu₂O_8+δ.

Abstract

Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over the <i>q_x-q_y</i> scattering plane in underdoped Bi₂Sr₂CaCu₂O_8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in the <i>q_x-q_y</i> scattering plane with radius equal to the magnitude of the charge order wave vector, <i>q</i>_CO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [<i>q_x</i> = ±<i>q</i>_CO, <i>q_y</i> = 0] and [<i>q_x</i> = 0, <i>q_y</i> = ±<i>q</i>_CO]) as the origin of the observed correlations.