Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane

Abstract: In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi$2$Sr$_2$CaCu$_2$O${8+\delta}$, a prototypical cuprate superconductor, to probe electronic correlations within the CuO$_2$ plane. We discover a dynamic quasi-circular pattern in the $x$-$y$ scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along $x$ and $y$ can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern.