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

F Boschini; M Minola; R Sutarto; E Schierle; M Bluschke; S Das; Y Yang; M Michiardi; Y C Shao; X Feng; S Ono; R D Zhong; J A Schneeloch; G D Gu; E Weschke; F He; Y D Chuang; B Keimer; A Damascelli; A Frano; E H da Silva Neto

doi:10.1038/s41467-020-20824-7

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

Nat Commun. 2021 Jan 26;12(1):597. doi: 10.1038/s41467-020-20824-7.

Authors

F Boschini^{1

2

3}, M Minola⁴, R Sutarto⁵, E Schierle⁶, M Bluschke^{4

6}, S Das⁷, Y Yang⁷, M Michiardi^{1

2

8}, Y C Shao⁹, X Feng⁹, S Ono¹⁰, R D Zhong¹¹, J A Schneeloch¹¹, G D Gu¹¹, E Weschke⁶, F He⁵, Y D Chuang⁹, B Keimer⁴, A Damascelli^{1

2}, A Frano⁷, E H da Silva Neto^{12

13

14}

Affiliations

¹ Quantum Matter Institute, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada.
² Department of Physics & Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada.
³ Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, Varennes, QC, J3X 1S2, Canada.
⁴ Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569, Stuttgart, Germany.
⁵ Canadian Light Source, Saskatoon, SK, S7N 2V3, Canada.
⁶ Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489, Berlin, Germany.
⁷ Department of Physics, University of California San Diego, La Jolla, CA, 92093, USA.
⁸ Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Straße 40, Dresden, 01187, Germany.
⁹ Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.
¹⁰ Central Research Institute of Electric Power Industry, Yokosuka, Kanagawa, 240-0196, Japan.
¹¹ Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY, USA.
¹² Department of Physics, University of California, Davis, CA, 95616, USA. eduardo.dasilvaneto@yale.edu.
¹³ Department of Physics, Yale University, New Haven, CT, 06511, USA. eduardo.dasilvaneto@yale.edu.
¹⁴ Energy Sciences Institute, Yale University, West Haven, CT, 06516, USA. eduardo.dasilvaneto@yale.edu.

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 Bi₂Sr₂CaCu₂O_8+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.