Peierls Semiconductor

The highly conductive class of solids based on TTF—TCNQ have less than complete charge transfer ( 0.6 electrons/unit for TTF—TCNQ) and display metallic behavior above a certain temperature. However, these solids undergo a metal-to-insulator transition and behave as organic semiconductors at lower temperatures. The change from a metallic to semiconducting state in these chain-like one-dimensional (ID) systems is a result of a Peierls instability. Although for tme one-dimensional systems this transition should take place at 0 Kelvin, interchain interactions lead to effective non-ID behavior and inhibit the onset of the transition (6). 

On the basis of these extensive studies, LiPt(mnt) behaves as a simple quasi-one-dimensional conductor with a mean-field-like metal—semiconductor transition due to the Peierls instability. 

Lio.5tPt S2C2(CN)2 2]-2H20.129 X-Ray studies reveal that the [Pt(mnt)2]05 anions are stacked face-to-face along the a axis of the unit cell to form a fourfold distorted linear chain. This can be regarded as the Peierls distorted state analogous to that found in Rbi 67[Pt(C204)2] H20. The room temperature conductivity (cr ) is 1 Q 1 cm-1 and the temperature dependence is that of a semiconductor.129... 

It is the Peierl s instability that is believed to be responsible for the fact that most CPs in their neutral state are insulators or, at best, weak semiconductors. Hence, there is enough of an energy separation between the conduction and valence bands that thermal energy alone is insufficient to excite electrons across the band gap. To explain the conductive properties of these polymers, several concepts from band theory and solid state physics have been adopted. For electrical conductivity to occur, an electron must have a vacant place (a hole) to move to and occupy. When bands are completely filled or empty, conduction can not occur. Metals are highly conductive because they possess unfilled bands. Semiconductors possess an energy gap small enough that thermal excitation of electrons from the valence to the conduction bands is sufficient for conductivity however, the band gap in insulators is too large for thermal excitation of an electron accross the band gap. 

Electrical conductivity measurements of the [TTF]2[Ni(edt)2] and [TTT ]12[Ni(edt)2] systems show them to be semiconductors with conductivities of 10-3 and 30 Q-1cm-1, respectively. In both compounds, the direction of highest conductivity is along the stacks of organic molecules. Since the [TTT]i.2[Ni(edt)2] system contains chains of partially oxidized organic molecules that appear to be uniformly spaced along the stacking axis, a high conductivity would be expected. The low room-temperature conductivity (compared with other partially oxidized TTT salts) and its temperature dependence, which is typical of a semiconductor, are presumed to be a consequence of the postulated Peierls distortion. 

Fig. 1.5. Transition from metallic behaviour with half-filled 7r-band to a bandgap semiconductor due to Peierls distortion...

Recently, the spectral study of DMTM(TCNQ)2 phase transition was performed [60]. The salt is a quarter-filled organic semiconductor containing segregated chains of TCNQ dimers and DMTM counterions. This material undergoes an inverted Peierls transition, which has tentatively been explained in terms of a crystal-field distortion. It was shown that the experimental values of unperturbed phonon frequencies and e-mv coupling constants are nearly independent of temperature. The dimer model fails to reproduce the phonon intensities and line shapes and underestimates the coupling constants, whereas the CDW model produces better results... 

From more recent optical data it is proved that Qn(TCNQ)2 is a semiconductor up to 300 K, with an energy gap due mainly to a Peierls distortion on the conducting TCNQ chains [57]. However, this gap Ec = 2A is not constant, as is simply assumed in the model of Epstein et al. In fact, A appears to decrease significantly from = 1200 K at T = 0 K to = 300 K at T = 300 K, somewhat like in the salt TEA(TCNQ)2 (see above). This requires a modified approach in which the existence of a conductivity maximum cjm still implies a T-dependent mobility p, but not so steep as would require a constant gap. 

In this salt (MDT = l-methyl-l,4-dithianium), there is a brick wall stacking arrangement of TCNQ dimers. It is a quasi-one-dimensional semiconductor up to 300 K with an energy gap Ec = 0.22 eV. The magnetic susceptibility follows quite well a Bonner-Fisher law with / = 76 K. At room temperature x = 9.5 x 10-4 emu/mol and there is a maximum = 14.5 x 10 4 emu/mol at Tm = 100 K. There is also a probable spin-Peierls transition at 5.5 K [64]. 

The salts of this series [BEDT-TTF = bis(ethylenedithiolo)tetrathiafulvalene], with X = AuBr2, CuCl2, or Ag(CN)2, are all semiconductors with narrow band widths and strong Coulomb repulsions. For this series the magnetic susceptibility has room-temperature values of = 8 to 9 x 10 4 emu/mol, and maximum values of = 16 to 18 x 10 4 emu/mol, at TM = 60 to 70 K. However, it does not fit well a Bonner-Fisher law in any case. A spin-Peierls transition is found to occur, at 7 K, for the Ag(CN)2 salt only [65]. 

Figure 1 also illustrates the fact that many of these anisotropic compounds undergo metal-semiconductor transitions below about 50 K [2]. For TTF-TCNQ, which was investigated intensively in the 1970s, diffuse x-ray scattering studies first showed conclusively that this was a Peierls transition [28]. There are, in fact, three phase transitions, at 53, 48, and 38 K. 

Structural change resulting from a Peierls distortion can have dramatic effects on the physical properties. Look at the half-filled bands of Figure 6.6. There is no HOMO-LUMO gap. Such a situation depicts a metallic electrical conductor. On the other hand, after Peierls distortion there is a band gap at the Fermi level (Figure 6.10) and the material, depending on the width of the gap, is a semiconductor or an insulator. For a semiconductor, thermal excitation of electrons from the... 

This problem contains elements of Exercises 6.4 and 6.5 that treat infinite CH and BN chains, respectively. Use the same approach. Instead of two 7t-band pairs there is only one for planar poly- -BHNH- and, as for poly-BN, there will be a band gap. With two 7t electrons per unit cell, the valence band is just filled. Hence, it would be a semiconductor and not subject to a Peierls distortion. 

Because of the softness of organic metals one expects them to show interesting behavior under applied pressures. This had been demonstrated earlier by Jerome and co-workers on several compounds and in the case of TMTSF-DMTCNQ (DMTCNQ = dimethyltetracyanoqui-nodimethane) a pressure of 10 kbar transforms it abruptly from a Peierls semiconductor with Tm = 50 K to a metal at all temperatures (91). When the temperature-dependent resistance of the (TMTSF)2X family became known, the very low transition temperatures in some of the compounds suggested that these salts would easily become metallic, and maybe even superconducting, under pressure. 

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