In this article, we review different experiments using advanced X-ray diffraction techniques, in particular coherent diffraction, which have enabled us to reveal the behavior of systems with broken symmetry such as charge density waves (CDW) and spin density waves (SDW), through their phase. After a brief introduction to the contribution of coherent X-rays in the field, we show how the method can be applied to these two phases of matter, in static and dynamic regimes. In particular, this approach has allowed us to probe the sliding state of CDW systems by observing them through their phase fluctuations, to which coherent X-rays are particularly sensitive. Several CDW compounds capable of slipping are presented, each with a unique and clearly pronounced signature. Two main characteristics emerge from this series of experiments that have been little addressed until now: the influence of CDW pinning by the sample surfaces and the propagation of periodic phase defects such as charge solitons through the sample. Phase models describing the spatial and temporal properties of ODCs in the sliding regime are presented in the last part of this review.
Figure 1: Illustration of the signature of sliding CDW obtained by coherent diffraction in two very distinct systems: the two-dimensional TbTe3 system and the quasi-one-dimensional NbSe3 system. Below the threshold current Is, the 2kF satellite reflection associated with the CDW widens considerably in NbSe3. B) This effect is due to the phase curvature effect expected when considering the wave pinned by the surface (the phase is then fixed on all edges using Dirichlet boundary conditions). Above the threshold, the satellite reflection tends to return to its initial condition with the disappearance of the diffraction fringes. C) This effect is linked to the nucleation of charged solitons, releasing the stresses and sliding on top of the CDW.
Tracking Defects of Electronic Crystals by Coherent X-ray Diffraction
David Le Bolloc’h, Ewen Bellec, Natacha Kirova and Vincent L. R. Jacques
Symmetry 2023, 15(7), 1449