# Visualizing the charge order and topological defects in an overdoped (Bi,Pb)$_2$Sr$_2$CuO$_{6+x}$ superconductor

## TL;DR

This study uses scanning tunneling microscopy to visualize charge order and topological defects in an overdoped cuprate superconductor, revealing their energy-dependent evolution and spatial dynamics.

## Contribution

It provides the first detailed visualization of topological defects in charge order in overdoped cuprates, linking defect behavior to energy and pseudogap phenomena.

## Key findings

- Charge order wavevector is non-dispersive with energy.
- Topological defects decrease in density and migrate with increasing energy.
- Pairs of defects can appear and disappear as energy varies.

## Abstract

Electronic charge order is a symmetry breaking state in high-$T_\mathrm{c}$ cuprate superconductors. In scanning tunneling microscopy, the detected charge-order-induced modulation is an electronic response of the charge order. For an overdoped (Bi,Pb)$_2$Sr$_2$CuO$_{6+x}$ sample, we apply scanning tunneling microscopy to explore local properties of the charge order. The ordering wavevector is non-dispersive with energy, which can be confirmed and determined. By extracting its order-parameter field, we identify dislocations in the stripe structure of the electronic modulation, which correspond to topological defects with an integer winding number of $\pm 1$. Through differential conductance maps over a series of reduced energies, the development of different response of the charge order is observed and a spatial evolution of topological defects is detected. The intensity of charge-order-induced modulation increases with energy and reaches its maximum when approaching the pseudogap energy. In this evolution, the topological defects decrease in density and migrate in space. Furthermore, we observe appearance and disappearance of closely spaced pairs of defects as energy changes. Our experimental results could inspire further studies of the charge order in both high-$T_\mathrm{c}$ cuprate superconductors and other charge density wave materials.