Electronic Properties of Inorganic Quasi-One-Dimensional Compounds: Part I — Theoretical

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This description is mainly based on the properties of transition metal trichalcogenides. The novel collective transport mechanism for electronic conduction, exhibited by some of the latter compounds — NbSe 3 being considered as the prototype — is surveyed according to a classical theory and a theory including macroscopic quantum effects.

In addition, the book contains a description of the properties of non-linear excitations, or solitons, in one-dimensional systems. Customer Reviews Average Review. See All Customer Reviews. Shop Textbooks. Add to Wishlist. Structures of K 0. Lateral phasing between the dipolar CDWs in a K 0.

The Ginzburg—Landau formalism introduced in section 2. The treatment of the inter-chain coupling term in the mean-field approximation leads a 3D Peierls transition at finite temperature. The variation of T P with W in the amplitude fluctuation regime is the same for complex- and real-order parameters. The dynamics of the amplitude and of the phase modes of the PLD of K 0. Phase and amplitude excitations are relatively well decoupled in energy: the amplitude mode is optic-like, while phase excitations are acoustic-like. For low-energy deformations, the variation of the amplitude of the order parameter can be neglected.

In this case, CDW deformations are described by an elastic medium involving continuous long-range deformations of the phase of the PLD for q close to. This assumption is however not valid when large stresses break phase continuity. In that case, plastic deformations nucleate dislocation loops. Also the variation of the amplitude of the order parameter cannot be neglected when large strains, induced for example by strong pinning centers, lead to the formation of Friedel oscillations FOs.

They also considered the deformation of the PLD in the presence of various imperfections using local models [ [67] ]. Their pioneering work will be illustrated by recent experimental findings. Such a regime where the CDW becomes extremely rigid occurs in K 0. Upon cooling K 0. This effect has been observed in K 0. Their anisotropy follows also the square of the anisotropy of CDW coherence length.

In real systems where the CDW is locally pinned to lattice defects see section 4. Note that 2 k F x varies linearly in the central part of the sample where 0. Adapted from Ref. Shear deformation of a sliding CDW pinned on a surface containing the chain direction. The local wave vector q CDW y , perpendicular to the bent CDW surface fronts, induces a tilt of 2 k F along the transverse direction y. These local shear deformations break the lateral coherence of the CDW sub-lattice.

This occurs via a so-called phase slippage phenomenon, which is probably achieved by nucleation and growth of edge loop dislocations [ [67] ]. However, it was only recently that an isolated CDW dislocation has been directly imaged using coherent X-ray diffraction in K 0. The recent observation of a well-defined multi-peak speckle spectrum in transverse reciprocal direction in the creep regime of NbSe 3 [ [75] ] shows that the loss of transverse coherence in the CDW sublattice polarized under the application of an electric field should be accompanied by nucleation of CDW dislocations that cause abrupt CDW phase shifts.

The top of the figure gives a representation of the PLD in direct space and the bottom of the figure shows the corresponding diffracted speckle spectra. Because of the tilting of the CDW wave vector q CDW with respect to chain direction, b , the dislocation mixes edge and screw wave front deformations from Ref. However, the detailed understanding of these electronic phenomena requires a microscopic description of the textured 3D PLD pattern in the presence of pinning centers, a question that is still incompletely settled.

The delicate question of CDW pinning by randomness begins to be addressed in the s for a recent review, see [ [79] ]. The most important effect occurs when defects, located on the conducting path, strongly perturb the 1D electronic motion. With the long-range elastic energy term previously considered in section 4. The phase shift that results from the forward scattering process elongates or compresses locally the phase of the CDW see Fig. As a function of the relative values of the pinning energy gain and of the elastic energy cost, two extreme situations are found: — when the individual pinning energy gain dominates, the phase of the CDW is adjusted on each impurity site Fig.

The coherence of the CDW pattern is broken by the randomness of the impurity distribution along both chain and transverse directions the phase adjustment on impurities induces local shear deformations of the CDW sub-lattice, which also break the optimal inter-chain phasing due to W. In the situation of strong pinning, each CDW coherent domain contains few impurities; — when the elastic energy cost dominates, there is collective adjustment of the phase of the CDW on the impurity distribution Fig.

The CDW pattern remains coherent in large domains containing a sizeable number of impurities. In this case the possibility to obtain a Bragg glass with a quasi-long-range CDW order has been considered [ [83] ]. CDW patterns for strong impurity pinning a , weak impurity pinning b and weak pinning between strongly pinned CDW domains c.

In a , the arrows show local shears of the CDW lattice due to individual phase adjustments on impurities. In a and b , the dots represent local impurities and in c the boxes materialize strongly pinned domains. Parts a and b are from Ref.

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The real texture of the pinned CDW pattern is more subtle than those of these two extreme descriptions. In particular, it was suggested on the basis of earlier structural studies of irradiated organic salts [ [84] ] that the CDW pattern could be the superimposition of weakly pinned regions, where the phase fluctuates slowly, and strongly pinned domains where the phase is locked Fig.

In this situation the domain walls play the role of pinning surface as a source of shear deformation of the CDW see Fig. Using this effect, it has been possible to follow upon heating the thermal de-pinning of the phase of the CDW by thermally excited phasons in doped K 0. From Ref. Earlier pinning theories ignored local variations of the phase Fig. Both charge screening of non-isoelectronic impurities by a phase shift not yet considered in the literature until recently [ [88] ] and amplitude [ [87] ] variation in response to an impurity potential are the two basic components of Friedel oscillations FOs.

Part b represents more specifically the induced 1D FO's of amplitude, u i 2 k F , in response to the impurity potential V imp. In response to strong lattice defects, such as those created by X-ray irradiation, 1D FOs can be induced well above.

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The phase shift is directly related to Z by the Friedel sum rule see also the contribution by J. Villain, M. Lavagna, and P. This last phase shift cancels the optimal Coulomb inter-chain coupling energy gain, W , in transverse direction see Fig. On large scales, there is thus charge neutrality of defects dressed by the FOs. Left part: experimental X-ray diffraction spectrum of K 0. Charge localization effects are also commonly observed in oxides and organic compounds of higher electronic dimensionality.

However, a mixture of bond and charge orders without inversion symmetry can lead to electronic ferroelectricity, as observed in some organic materials [ [93] ], and could drive multiferroicity in several classes of materials [ [94] , [95] ]. Another field of current interest concerns the presence of CDW instability in 2D and 3D electronic systems. It has also been proposed that the crystal structure of some group V and VI simple elements and A V B VI compounds could be stabilized by a Peierls-like transition occurring in a prototype 3D cubic lattice, where there is an anisotropic overlap of the p-wave functions see, for example, [ [98] ].

Note that H. Jones was the first to propose in [ [4] ] a similar stabilization mechanism for Bi; see also R. Peierls [ [1] ] for the column V elements. However, such a mechanism could be questioned [ [99] ] if the s—p hybridization which blurs the 1D nature of the orbital overlap cannot be neglected. This is apparently not the case for column-V, -VI and -VII elements, where the s—p hybridization is very small see the contribution of J.

Gaspard in this issue. However, the origin of these CDW transitions cannot be simply rationalized by a simple FS nesting mechanism. This leaves open the possibility of CDW instabilities driven by strong electron—phonon coupling mechanisms. CDW transitions are also observed in 3D electronic systems. Complex spin, charge and orbital current modulations are also observed in 2D superconducting cuprates. Good candidates for such transitions could be the incompletely nested semi-metallic oxides and bronzes [ [97] ]. In most of them, superconductivity develops under pressure at the vanishing point of the density-wave ground state.

This situation is well illustrated by organic conductors [ [] , [] ]; see also the contribution of D. However, in multiband conductors or when Fermi level states of a single-band conductor are not completely removed by the nesting process, superconductivity could coexist with the CDW modulation. Coexistence between CDW and superconductivity is observed in cuprates, in 1T—TiSe 2 and in the multiband charge transfer organic conductor TTF[Ni dmit 2 ] 2 see [ [41] ] and earlier references therein. This paper is written in memory of Prof. Jacques Friedel who has always considered the physics of low-dimensional conductors as resulting from a subtle interplay between electronic and structural degrees of freedom.

The author recognizes more than 40 years of live discussions with him on that topic. Here I want to especially acknowledge our last discussions concerning the history of the Peierls transition. The part on phonon dynamics of the Peierls transition is built on discussions with the late H. Some ropes have paced to get seen with starting, while right as interested, this campus styleComing of in some places.

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