Incommensurate charge density waves (CDW) have the extraordinary ability to display non-Ohmic behavior when submitted to an external field. The mechanism leading to this non trivial dynamics is still not well understood, although recent experimental studies tend to prove that it is due to solitonic transport. Solitons could come from the relaxation of the strained CDW within an elastic-to-plastic transition. However, the nucleation process and the transport of these charged topological objects have never been observed at the local scale until now. In this letter, we use in-situ scanning x-ray micro-diffraction with micrometer resolution of a NbSe$_3$ sample designed to have sliding and non-sliding areas. Direct imaging of the charge density wave deformation is obtained using an analytical approach based on the phase gradient to disentangle the transverse from the longitudinal components over a large surface of a hundred microns size. We show that the CDW dissociates itself from the host lattice in the sliding regime and displays a large transverse deformation, ten times larger than the longitudinal one and strongly dependent on the amplitude and the direction of the applied currents. This deformation continuously extends across the macroscopic sample dimensions, over a distance 10 000 times greater than the CDW wavelength despite the presence of strong defects while remaining strongly pinned by the lateral surfaces. This 2D quantitative study highlights the prominent role of shear effect that should play a significant role in the nucleation of solitons.
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