Peierls state

As mentioned in Section II, LRO in two dimensions can exist only for a real order parameter, that is, for CDW in a half-filled band. This would be the case for BOW in the polymers or the Peierls state, which would be stabilized by transverse hopping or interchain coupling. This is also the case of the CDW state of the n = 1 two-dimensional Hubbard model. All other types of instabilities, such as those treated in the RPA previously in Section V, require three-dimensional coupling to stabilize any LRO. 

At T, the system becomes two-dimensional and will undergo a transition to a spin-Peierls state at lower temperature due to the RG-generated BOW interchain interaction Vcdw- The static uniform magnetic susceptibility vanishes exponentially in this state made of local spin-singlet pairs. The... 

In solids with strong localization of the charge carriers, there are no charge degrees of freedom, but there will be spin degrees of freedom. In this class we should include systems that underwent a metal-insulator transition for a 4kF CDW state. The ground states of these systems are usually 2kF spin density wave or spin-Peierls states. 

The linewidth, AHpp, should follow the temperature dependence of the resistivity, and therefore decrease at low T in the metallic regime. For TTF-TCNQ, AHpp increases by factor of 3 between 300 and 60 K, but TTF-TCNQ is a special case since there are two chains each with paramagnetic species. AHpp and tj1 derived from NMR in TTF-TCNQ behave similarly in the conducting region. The drop in AHpp observed in the Peierls state (T < 54 K) is due to the vanishing of the density of states, D(EF), which is required for electron scattering. 

When the strong Coulomb repulsion works between electrons, the electrons are regarded as localized particles. In one-dimension the localized spins can undergo a magnetic transition either to an anti-ferromagnetic state or a Spin Peierls state that has no spin [69]. 

When magnitude of the electron-electron Coulomb interaction increases, the system is expected to show a ehange from the SDW dominated state to the spin-Peierls one. This was verified in another system, (TMTTF(tetramethyltetra-thiafulvalene))2X and (TMTSF)2X [74]. The former materials have the narrower band width than the latter. This means that the role of Coulomb interaction is more important in the former system than in the latter. The former system is expected to have the spin-Peierls state and the latter one the SDW state. Systematic studies have proposed the phase diagram shown in Fig. 23 [74]. 

We present a detailed calculation of the transition temperature of a model, filamentary excitonic superconductor. The proposed structure consists of a linear chain of transition-metal atoms to which is complexed a ligand system of highly polarizable dye molecules. The model is discussed in the light of recent developments in our understanding of one-dimensional metals. We show that for the structure proposed, the momentum dependence of the exciton interaction results in the superconducting state being favoured over the Peierls state, and in vertex corrections to the electron-exciton interaction which are small. The calculation of the transition temperature is based on what we believe to be reasonable estimates of the strength of the excitonic interaction, Coulomb repulsion and band structure. 

In the case of the CP state, where an unpaired electron exists at the M " site per dimer unit, no cell doubling occurs and so either a Mott-Hubbard insulator or a one-dimensional metal is expected. Conversely, the electronic structures of the CDW state and the ACP state are regarded as Peierls and spin-Peierls states, respectively [178,184,185]. The four states of the MMX complexes are distinguished by the valence states of the metal and the bond distances in the crystal structure. 

The main problem is the competition between these different instabilities. A departure from ideal 1-D situation, by increasing the transverse interactions, will suppress the Peierls state, as described by a mean-field approach [29]. Nevertheless, this description does not strictly apply to these low-dimensional systems, where large fluctuative regimes are present, as observed by diffuse X ray techniques [13,30]. 

As above mentioned, the displacement of halogen atoms from the midpoints between neighbouring metal ions brings on the doubly degeneracy, that is, the Peierls state, in the chain, so that the breathing mode of halogen... 

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