# Evolution of charge order topology across a magnetic phase transition in cuprate superconductors

## TL;DR

This study reveals how the momentum space topology of charge correlations in electron-doped cuprates evolves across a magnetic phase transition, showing a transition from full rotational symmetry to bond-oriented order, linked to Fermi surface changes.

## Contribution

It uncovers the evolution of charge order topology in cuprates across a magnetic transition, including a previously unobserved symmetric phase, and connects these changes to Fermiology and phase diagram revisions.

## Key findings

- Charge correlations initially exhibit full rotational symmetry in momentum space.
- Charge order orientation locks to Cu-O bonds at higher doping levels.
- The topology evolution correlates with an antiferromagnetic quantum phase transition.

## Abstract

Charge order is now accepted as an integral constituent of cuprate high-temperature superconductors, one that is intimately related to other instabilities in the phase diagram including antiferromagnetism and superconductivity. Unlike nesting-induced Peierls-like density waves, the charge correlations in the CuO2 planes have been predicted to display a rich momentum space topology depending on the detailed fermiology of the system. However, to date charge order has only been observed along the high-symmetry Cu-O bond directions. Here, using resonant soft X-ray scattering, we investigate the evolution of the full momentum space topology of charge correlations in Ln2CuO4 (Ln=Nd, Pr) as a function of intrinsic electron doping. We report that, upon electron doping the parent Mott insulator, charge correlations first emerge in a hitherto-unobserved form, with full (Cinf) rotational symmetry in momentum-space. At higher doping levels, the orientation of charge correlations is sharply locked to the Cu-O bond high-symmetry directions, restoring a more conventional bidirectional charge order with enhanced correlation lengths. Through charge susceptibility calculations, we closely reproduce the drastic evolution in the topology of charge correlations across an antiferromagnetic quantum phase transition, highlighting the interplay between spin and charge degrees of freedom in electron-doped cuprates. Finally, using the established link between charge correlations and the underlying fermiology, we propose a revised phase diagram of Ln2CuO4 with a superconducting region extending toward the Mott limit.