Transition, Peierls

In 1955, R. E. Peierls (334) pointed out the inherent instability of a one-dimensional metal such as K2Pt(CN)4Bro.3(H20)3. In analogy with the Jahn- 

Theoretical studiesof the Peierls distortion showthat within mean field theory its presence can be a function of temperature (261, 347, 349). This leads to a transition from a band metal to a band semiconductor/insulator as the temperature is lowered below the transition temperature, Tp, termed the Peierls transition. The characterization of the metal-insulator transition in KsPt(CN)4-Bro.3(H20)s as a Peierls transition has triggered much of the increased work on the theory of the Peierls transition. 

The transition arises dynamically through the interaction between the electrons and the quantized lattice vibrations of the solid, phonons (437). The phonons, in a manner similar to electrons, are assigned a wavevector q = 2jt/A where k is the wavelength of the lattice vibration. There is an energy associated with each phonon of wavevector q, as indicated schematically in Fig. 12. The actual dispersion relation is a function of the mass of the atoms in a 

There has been speculation that anomalous electrical behavior may accompany a Peierls transition. In particular, the presence of a soft phonon mode at 

---

It is well known that metallic electronic structure is not generally realised in low-dimensional materials on account of metal-insulator transition (or Peierls transition [14]). This transition is formally required by energetical stabilisation and often accompanied with the bond alternation, an example of which is illustrated in Fig. 4 for metallic polyacetylene [15]. This kind of metal-insulator transition should also be checked for CNT satisfying 2a + b = 3N, since CNT is considered to belong to also low-dimensional materials. Representative bond-alternation patterns are shown in Fig. 5. Expression of band structures of any isodistant tubes (a, b) is equal to those in Eq.(2). Those for bond-alternation patterned tube a, b) are given by. 

Fig. 4. Peierls transition in metallic polyacetylene and accompanied generation of bond alternation. Note that the semiconductive (or insulating) structure accompanied with the bond alternation is the more energetically stable.

A couple of theoretical studies [5,19] have hitherto attempted to estimate the Peierls transition temperature (Tp) for metallic CNT. A detailed theoretical check with respect to the stability of metallic wavefunction in tube (5, 5) has also... 

It will be intriguing to theoretically examine the possibility of superconductivity in CNT prior to the actual experimental assessment. A preliminary estimation of superconducting transition temperature (T ) for metallic CNT has been performed considering the electron-phonon coupling within the framework of the BCS theory [31]. It is important to note that there can generally exist the competition between Peierls- and superconductivity (BCS-type) transitions in lowdimensional materials. However, as has been described in Sec. 2.3, the Peierls transition can probably be suppressed in the metallic tube (a, a) due to small Fermi integrals as a whole [20]. 

This model, which is sometimes referred to as the Fluctuating Gap Model (FGM) [42], has been used to study various aspects of quasi-one-dimensional systems. Examples arc the thermodynamic properties of quasi-one-dimensional organic compounds (NMP-TCNQ, TTF-TCNQ) [271, the effect of disorder on the Peierls transition [43, 44, and the effect of quantum lattice fluctuations on the optical spectrum of Peierls materials [41, 45, 46]. 

Radicals have been known for many years to form organic paramagnetic materials with numerous magnetic properties (ferro- or ferri-magnetism, spin Peierls transition, spin frustration, spin ladder systems) (see [51-60] for verdazyl radicals, [61-68] for thiazyl radicals, [69] for nitronyl nitroxide and [70-78] for Tempo radicals) (Fig. 6). When they are in their cationic form, they are valuable candidates for an association with the M(dmit)2 systems they will then provide the magnetic properties thanks to their free electron(s), whereas the M(dmit)2 moieties will provide the electrical properties. 

As already discussed in Chapter 1, this kind of mixed valence salt becomes conductive due to the transfer of one electron from two BEDT-TTF molecules to the anion layers. However, at the surface, the charge can become unbalanced, resulting is an incomplete CT. This leads to differentiated surface vs. bulk nesting vectors and to the existence of surface CDWs (Ishida et al, 1999). The Peierls transition has also been observed on the a -planes of single crystals of TTF-TCNQ with a variable temperature STM (Wang et al, 2003) and will be discussed in Section 6.1. 

Computations using the crystal structure at 60 K, just above the Peierls transition, as well as at RT and 4.6 kbar show no relevant changes in the band structure except for a small expected increase in die dispersion along the chain direction (Fraxedas etal., 2003). 

Figure 6.7. High-resolution ARUPS spectta measured at kp (hco = 21.2 eV) above (70 K) and below (30 K) the Peierls transition. The solid line spectrum corresponds to Ep, as determined for a silver film. Note that the spectrum follows the shape given by Eq. (1.27). Reprinted with permission from F. Zwick, D. Jerome, G. Margaritondo, M. Onellion, J. Voit and M. Grioni, Physical Review Letters, 81, 2974 (1998). Copyright (1998) by the American Physical Society.

A detail of the p(T) curve is displayed for sample 3 in Fig. 6.36. The non-linear increase of resistivity below c. 50 K corresponds to the metal-insulator Peierls transition. The Peierls transition is more readily observed for the Ea — 273.7 K sample because of its lower activation energy as compared to the c. Ea — 296 K samples. 

Figure 6.36. Detail of the /o(T ) curve for 3 showing the Peierls transition. The dashed line corresponds to a linear interpolation of the higher temperature region. Reprinted from Journal of Solid State Chemistry, Vol. 168, J. Fraxedas, S. Molas, A. Figueras, I. Jimenez, R. Gago, R Auban-Senzier and M. Goffman, Thin films of molecular metals TTF-TCNQ, 384-389, Copyright (2002), with permission from Elsevier.

Karutz FO, von Schutz JU, Wachtel H, Wolf HC (1998) Optically reversed Peierls transition in crystals of Cu(dicyanoquinonediimine)2. Phys Rev Lett 81 140-143... 

Highly conducting 1-D system. Undergoes a Peierls transition at low temperature. Nearly superconducting. Stack of super-positioned, square-planar Pt(CN)4 groups. 

According to the factor-group analysis, there are 18 Raman and 9 IR active new vibrational modes in the low-temperature structure of CuGe03, below the temperature of the spin-Peierls transition Tc=14 K. While two of the Raman-active folded modes were clearly observed in the very first optical experiments, no traces of the IR folded modes could be found for a long time. We have observed IR folded modes for the first time, measuring... 

Fig. 10. Illustration of the molecular displacements occurring in the a,-Cp plane in [TTF] [Cu(tfd)2] below the spin-Peierls transition temperature of 12 °K. Only the [TTF]+ units are shown for clarity however, the translation of the center of mass of the [Cu(tfd)2] units is indicated (Ref. 51)...

An additional feature of the temperature dependent X-ray scattering is the persistence above Tc of intensity at the superlattice positions51). This is consistent with a soft phonon mode at a wave vector commensurate with the changes that occur on dimerization. It has been suggested that this low frequency lattice mode may be a requirement for the observation of a spin-Peierls transition. 

---