The transport of charges through materials is an essential phenomenon for many devices, whether they are semiconductors, superconductors or batteries. Unfortunately, it is not possible to observe the motion of charges passing through a crystal using X-rays because of their low sensitivity to almost free electrons. On the other hand, in so-called “Charge Density Waves” (CDW) systems, the transport of charges is accompanied by a deformation of the atomic lattice, which can be observed by X-rays.
Electronic transport in these materials has been observed through the behavior of the underlying atomic lattice using an intense X-ray beam generated by a Free Electron Laser (XFEL). In charge density wave systems, the electrons and the atomic lattice exhibit a wave-like behavior, the two modulations being inseparable. This phase of matter is very sensitive to various external excitations, such as changes in temperature, an ultrashort laser pulse or even weak currents. In the latter case, when a direct current above a critical threshold is applied to the sample, an additional current appears in the crystal. It is naturally pulsed and is directly linked to the behavior of the CDW. This effect is explained by a CDW deformation under current, eventually breaking beyond a certain deformation limit and periodically releasing charged topological objects that travel over macroscopic distances. This phenomenon has been observed thanks to the coherent and extended X-ray beam generated from the LCLS XFEL source at Stanford. The CDW phase was deduced from the diffraction patterns by applying a genetic algorithm. The CDW exhibits astonishing spatial coherence despite its nanometer period. It continuously deforms from one edge of the crystal to the other, which is several tens of microns wide. Like a guitar string plucked at both ends that bends under the effect of a force, the wave bends under the effect of the current pinned by the two side surfaces of the crystal. This shearing effect increases as the current increases, then suddenly relaxes above the threshold current (see figure 1). The wave deforms in the transverse direction by shear but also in the longitudinal direction, like an accordion that contracts and expands (see figure 2). The two types of deformation, transverse and longitudinal, are closely coupled, with the relaxation of one above the threshold leading to the appearance of the other. In addition, the steps on the crystal surface also act as traps, preventing it from slipping (see the two arrows on Fig.1). This result illustrates the capabilities of the new XFEL sources which, combined with appropriate analysis methods, open up new perspectives for observing and understanding the behavior of electronic systems.
Figure 1: (Top) X-ray diffraction pattern showing the satellite reflection associated with the CDW as a function of the current injected into the crystal. We observe a sudden elongation of the diffraction peak in the transverse direction as the threshold current (Is=0.8mA) is approached, followed by a slow relaxation as the current increases. (Bottom) Image of the CDW reconstructed from the diffraction patterns in the previous figure. The distance between two wave fronts is actually 14Å and has been considerably enlarged for clarity and to bring it closer to the height of the image, which corresponds to the width of the crystal of 40µm. The electronic modulation (wave fronts in yellow) curve more and more as the current increases. Above the threshold current, the wave fronts depin from the lateral surfaces of the crystal. The curvature then decreases and the stresses relax, except on the steps present on the sample surface on which the wave remains pinned (represented by the blue arrows).
Figure 2: Longitudinal (blue dots) and transverse shear (red dots) deformation as a function of the applied current. The position of the threshold current is indicated by the red dotted line. The inset is a close-up of small currents below the threshold, corresponding to the framed area (blue dotted area), highlighting the contrast between the exponential increase in shear and the longitudinal strain, which remains unchanged.
The importance of shear on the collective charge transport in CDWs revealed by an XFEL source,
David Le Bolloc’h, Ewen Bellec, Darine Ghoneim, Antoine Gallo-Frantz https, Pawel Wzietek, Luc Ortega, Anders Madsen, Pierre Monceau, Mathieu Chollet, Isabel Gonzales-Vallejo, Vincent L. R. Jacques, and Aleksandr Sinchenko, Sci. Adv., 11, eadr6034 (2025)
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Highlight CNRS février 2025 : https://www.inp.cnrs.fr/fr/cnrsinfo/cisaillement-dune-onde-de-densite-de-charge-observe-par-une-source-xfel