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Electronic charge order is a symmetry breaking state in high-$T_\mathrm{c}$cuprate superconductors. In scanning tunneling microscopy, the detectedcharge-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 scanningtunneling microscopy to explore local properties of the charge order. Theordering wavevector is non-dispersive with energy, which can be confirmed anddetermined. By extracting its order-parameter field, we identify dislocationsin the stripe structure of the electronic modulation, which correspond totopological defects with an integer winding number of $\pm 1$. Throughdifferential conductance maps over a series of reduced energies, thedevelopment of different response of the charge order is observed and a spatialevolution of topological defects is detected. The intensity ofcharge-order-induced modulation increases with energy and reaches its maximumwhen approaching the pseudogap energy. In this evolution, the topologicaldefects decrease in density and migrate in space. Furthermore, we observeappearance and disappearance of closely spaced pairs of defects as energychanges. Our experimental results could inspire further studies of the chargeorder in both high-$T_\mathrm{c}$ cuprate superconductors and other chargedensity wave materials.

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