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

F Boschini ,Y D Chuang,E Schierle,E Weschke,M Minola,A Damascelli,B Keimer,Xuefei Feng ,Feizhou He ,Ruidan Zhong ,Genda Gu ,John Schneeloch ,Shimpei Ono ,Martin Bluschke ,Matteo Michiardi ,Sanjib Das ,Yi-Feng Yang ,Alex Frañó ,Ronny Sutarto ,Yu‐Cheng Shao ,Eduardo H Da Silva Neto

doi:10.1038/s41467-020-20824-7

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 Bi2Sr2CaCu2O8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO2 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.

Highlights

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
Since the majority of the q-dependent RXS signal originates from orbital and charge-transfer excitations at a relatively highenergy loss (E > 0.9 eV, HE), the ability to resolve the charge order (CO) correlations is significantly improved by isolating the low-energy region (E < 0.9 eV, LE), which is possible with RIXS
The signal seems to persist beyond the underdoped regime, which has been suggested as evidence of strong correlations driving the CO38

Summary

Introduction

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. 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. Aiming to better understand the spatial and dynamic behavior of electron correlations in the cuprates, we carried out a series of resonant x-ray scattering (RXS) experiments across a range of temperature and doping values in Bi2Sr2CaCu2O8+δ (Bi2212) This is the ideal cuprate for our experiments since its band structure parameters and Fermi surface topology are well known from angle-resolved photoemission spectroscopy. We discuss temperatureand doping-dependent experiments that reveal the nuanced effects of the lattice potential, discommensurations and doping to the stabilization of dynamic charge correlations, providing a comprehensive picture of charge order formation in a cuprate

Methods

Results

Conclusion