This article reviews the static and dynamic properties of spontaneous superstructures formed by electrons. Representations of such electronic crystals are charge density waves (CDW) and spin density waves in inorganic as well as organic low-dimensional materials. A special attention is paid to the collective effects in pinning and sliding of these superstructures, and the glassy properties at low temperature. Charge order and charge disproportionation which occur in organic materials resulting from correlation effects are analysed. Experiments under magnetic field, and more specifically field-induced CDWs are discussed. Properties of meso-and nanostructures of CDWs are also reviewed.

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Electronic crystals: an experimental overview

Experimental studies of structurally incommensurate crystal phases

Through detailed examination of the crystal structure and bonding conditions in the trichalcogenides, it has been possible to gain a deeper understanding of the band structure of these complex materials, and with this of their unusual electronic behavior. The character of the observed semimetallicity in Ta${\mathrm{Se}}_{3}$ and Nb${\mathrm{Se}}_{3}$ is much clarified. Each material in the group-V family is seen to achieve a very individually tailored band structure, enfolding the various structural and energy-level adjustments. The nonuniformity and the molecularization of these structures contrasts strongly with the dichalcogenide behavior. The structural, if not the electronic, dimensionality of the group-V trichalcogenides remains closer to two than to one. It is found that the periodic structural distortions developed by Nb${\mathrm{Se}}_{3}$ are probably more suited to a metal-metal bonding description than to the traditional Fermi surface determined instability of a charge-density wave. The field-induced sliding of these distortions can then be described in terms of cooperative bond flipping through a discommensurate superlattice. We examine in crystal chemical terms why this motion is so unusually weakly pinned to defects and impurities in Nb${\mathrm{Se}}_{3}$. In fact, the investigation shows that it will be very hard to find a material better suited to the realization of this phenomenon.

Bands, bonds, and charge-density waves in the Nb Se 3 family of compounds

Strong electron correlations are at the heart of many physical phenomena of current interest to the condensed matter community. Here we present a survey of the mechanisms underlying such correlations in charge density wave (CDW) systems, including the current theoretical understanding and experimental evidence for CDW transitions. The focus is on emergent phenomena that result as CDWs interact with other charge or spin states, such as magnetism and superconductivity. In addition to reviewing the CDW mechanisms in 1D, 2D, and 3D systems, we pay particular attention to the prevalence of this state in two particular classes of compounds, the high temperature superconductors (cuprates) and the layered transition metal dichalcogenides. The possibilities for quantum criticality resulting from the competition between magnetic fluctuations and electronic instabilities (CDW, unconventional superconductivity) are also discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/79/8/084505/pdf

Charge density waves in strongly correlated electron systems.

The increase in energy of the sp anionic band on going from oxides to the less electronegative sulfides, selenides, or tellurides (with a similar trend in neighboring columns) facilitates anion–cation redox interactions involving the d levels of transition metal cations and the sp levels of anionic species. The interactions can induce phase transitions or gradual change within a given structural model. When a cation is reduced by electron transfer to its d levels from the sp band, holes appear at the top of the latter. Interesting soft chemistry can be carried out based on redox processes that neutralize the holes with electrons. This approach also allows particular structural types to be stabilized. Three structural domains can be recognized amongst the transition elements: 1) on the left-hand side of the periodic table layered structures are observed involving M4+ and (chalcogen)2- ions; 2) formation of sets of metal-metal bonds is then observed, the geometry of which depends on both the initial electron population and the electron transfer to the metal; 3) on the right-hand side the metals in their highest oxidation state are no longer active, and the holes at the top of the sp band are taken up by a catenation of the anions, which can lead to full polymerization of the anionic sublattice.

Anion–Cation Redox Competition and the Formation of New Compounds in Highly Covalent Systems

The crystal structure of NbSe3 has been refined from single crystal X-ray diffraction data. It has a monoclinic symmetry with lattice parameters: a=10.009 AA, b=3.4805 AA, c=15.629 AA, beta =109.47 AA, space group P21/m and six formulae per unit cell. The crystal structure of NbSe3 as determined at 100K shows that the 145K transition in the electrical resistivity is not accompanied by a structural distortion. Except for the decrease due to thermal contraction all interatomic distances are found to be the same. This is compatible with the proposed model of the charge-density-waves formation which has been put forward in order to explain the physical properties of the 145K transition. Electron diffraction pictures taken above and below the transition give direct evidence of the charge-density-waves formation at the transition. At 120K in agreement with Tsutsumi et al. (1977) the pictures contain superstructure spots at the (h,k+or-0.243, l) positions. Contrary to what has been reported by the same authors, the authors have found that at 3K above the transition the electron diffraction pictures do not contain the diffuse scattering streaks corresponding to the planes at k'=k+or-0.243, which would indicate fluctuations of the CDW above the transition.

http://iopscience.iop.org/article/10.1088/0022-3719/11/20/009/pdf

Charge-density waves in NbSe3 at 145K: crystal structures, X-ray and electron diffraction studies

The new tetrachalcogenide compounds have a one-dimensional structure and two of these show transport properties which are characteristic of this type of conductor. The authors electron microscopy study permits them to show clearly and characterise the charge density waves which appear at 263 and 285K in (TaSe4)2I and (NbSe4)103/I respectively. Moreover, they describe the behaviour of (TaSe4)3I and (NbSe4)3I when the temperature changes. These compounds undergo a space group change around 200 and 280K respectively. The results are connected to those obtained in other works by the study of transport phenomena or by band scheme calculations.

https://iopscience.iop.org/article/10.1088/0022-3719/17/17/007/pdf

Electron microscopy study of transition-metal tetrachalcogenide (MSe4)nI (M=Nb, Ta)

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R Ayroles

Papers

Charge-density waves in NbSe3 at 145K: crystal structures, X-ray and electron diffraction studies

Electron microscopy study of transition-metal tetrachalcogenide (MSe4)nI (M=Nb, Ta)

Incommensurate-commensurate transition in TaS3