In this article, we review different studies based on advanced X-ray diffraction techniques—especially coherent X-ray diffraction—that allowed us to reveal the behaviour of such symmetry-breaking systems as Charge Density Wave (CDW) and Spin density Wave (SDW), through their local phase. After a brief introduction on the added value of using coherent X-rays, we show how the method can be applied to CDW and SDW systems, in both static and dynamical regimes. The approach allowed us to probe the particular sliding state of CDWs systems by observing them through their phase fluctuations, to which coherent X-rays are particularly sensitive. Several compounds stabilizing a CDW phase able to slide are presented, each with a different but clearly pronounced signature of the sliding state. Two main features emerge from this series of experiments which have been little treated until now, the influence of CDW pinning by the sample surfaces and the propagation of periodic phase defects such as charge solitons across the entire sample. Phase models describing the spatial and temporal properties of sliding CDWs are presented in the last part of this review.

Charge and spin density waves are typical symmetry broken states of quasi one-dimensional electronic systems. They demonstrate such common features of all incommensurate electronic crystals as a spectacular non-linear conduction by means of the collective sliding and susceptibility to the electric field. These phenomena ultimately require for emergence of static and transient topological defects: there are dislocations as space vortices and space-time vortices known as phase slip centers, i.e., a kind of instantons. Dislocations are statically built-in under a transverse electric field; their sweeping provides a conversion among the normal carriers and condensate which ensures the onset of the collective sliding. A special realization in a high magnetic field, when the density wave is driven by the Hall voltage, originated by quantized normal carriers, reveals the dynamic vorticity serving to annihilate compensating normal and collective currents. Spin density waves, with their rich multiplicative order parameter, bring to life complex objects with half-integer topologically bound vorticities in charge and spin degrees of freedom. We present the basic concepts and modelling results of the stationary states and their transient dynamics involving vorticity. The models take into account multiple fields in their mutual non-linear interactions: the complex order parameter, the self-consistent electric field, and the reaction of normal carriers. We explore the traditional time-dependent Ginzburg–Landau approach and introduce its generalization allowing the treatment of intrinsic normal carriers. The main insights and illustrations come from numerical solutions to partial differential equations for the dissipative dynamics of one and two space dimensions.

Six decades ago, the scientist from Stanford University, W.P. Little, announced a crusade to search for superconductivity, assumed to be heat-resistant in organic materials. Although such an ambitious goal was never realized in practice, this proposal gave rise to the entire ecosystem of studies on “synthetic metals,” creating a diverse community of material, experimental, and theoretical activities in low-dimensional electronic systems. We shall briefly review some key steps in this history, examine its main branches, and recall the consequences that remain on the agenda today. Particularly, we shall focus on a phenomenon of electronic ferroelectricity, whose roots can be found in the suggestion of a would-be superconducting polymer.

Most of correlated electronic systems possess ground states with broken crystal symmetries

Phase transformations induced by short optical pulses are mainstream in studies on the dynamics of cooperative electronic states. We present a semiphenomenological modeling of spatiotemporal effects expected when optical excitons are intricate with the order parameter such as in, e.g., organic compounds with neutral-ionic ferroelectric phase transitions. A conceptual complication appears here, where both the excitation and the ground state ordering are built from the intermolecular electronic transfer. To describe both thermodynamic and dynamic effects on the same root, we adopt, for the phase transition, a view of the excitonic insulator—a hypothetical phase of a semiconductor that appears if the exciton energy becomes negative. After the initial pumping pulse, a quasi-condensate of excitons can appear as a macroscopic quantum state that then evolves, while interacting with other degrees of freedom which are prone to an instability. The self-trapping of excitons enhances their density, which can locally surpass a critical value to trigger the phase transformation. The system is stratified in domains that evolve through dynamical phase transitions and may persist even after the initiating excitons have recombined.