Soliton band solitons

The soliton conductivity model for rrans-(CH) was put forward by Kivelson [115]. It was shown that at low temperature phonon assisted electron hopping between soliton-bound states may be the dominant conduction process in a lightly doped one - dimensional Peierls system such as polyacetylene. The presence of disorder, as represented by a spatially random distribution of charged dopant molecules causes the hopping conduction pathway to be essentially three dimensional. At the photoexitation stage, mainly neutral solitons have to be formed. These solitons maintain the soliton bands. The transport processes have to be hopping ones with a highly expressed dispersive... 

Finally, let us just recall that the VEH method, and others as well, have been used to study the evolution of gap states into polaron or soliton bands, for example, upon doping [146] (see, e.g., Ref. 204 for trans-PA and PT). 

Using this model, the doping of polyacetylene proceeds by the interaction of dopants with solitons initially present in the polymer, then by polaron formation and at even higher doping levels by soliton formation. The soliton states then broaden into a soliton band that eventually fills the gap, giving a continuum of energy levels and a metallic state. 

A lattice of charged solitons (Figure 5.21) is obtained at about 4 mol% doping. At metallic conductivity, the soliton band overlaps the entire band gap between the valence band and the conduction band so that unpaired electrons with spin can contribute to the conductivity. This occms at 11% doping of trflMS-polyacetylene. 

Polyacetylene, becomes ionized after doping if the dopants are electron acceptors, or it receives extra electrons if the dopant represents an electron donor (symbolized by D+ in Fig. 9.12). The perfect polyacetylene exhibits the bond alternation discussed above, but it may be that we have a defect that is associated with a region of changing rhythm" (or phase ) from (— — = — =) to (— = — = —). Such a kink is sometimes described as a soliton wave (Fig. 9.12a,b) i.e., a solitary wave first observed in the 19th century in Scotland on a water channel, where it preserved its shape while moving over a distance of several kilometers. The soliton defects cause some new energy levels ( solitonic le >els ) to appear within the gap. These levels too form their own solitonic band. 

An important conclusion follows, namely that solitons, as well as polarons and bipolarons, cannot be distinguished in the IR spectrum, since all produce strong polarisation of the Id-lattice, and all produce vibrational coupling, as described by eq. 14. The naming of the doping-induced infrared bands as "soliton bands" is, then, misleacfing [20, 37]. 

Conwell and others have proposed that when long-range Coulomb interactions and screening are taken into account, the soliton band in tran5-(CH) overlaps the valence and conduction bands, giving a metallic state [52,53]. In contrast, Kivelson and Salkola have focused on the interchain... 

SoKtons produced in polyacetylene are delocalized over approximately 12 CH units, with the maximum charge density to the dopant counterion. Soliton formation results in the creation of a new localized electronic state which is in the middle of the energy gap. At a high level of doping the charged sohtons produce soliton bands that can merge to behave hke a metalhc conductor. 

Truong, V. T, Ennis, B. C., and Forsyth, M., Enhanced thermal properties and morphology of ion-exchanged polypyrrole films. Polymer, 36, 1933-1940 (1995). Kivelson, S., Electron hopping in a soliton band conduction in lightly doped (CH)., Phys. Rev. B, 25, 3798-3821 (1982). 

According to Stafstrom [85], in the lightly doped regime the dopant potentials stabilize the soliton states and increase the gap between the occupied soliton band and the conduction band. In the heavily doped regime, the dopant potential effect favors a low-band-gap system. Moreover, lattice fluctuations and disorder are not expected to completely destroy the soliton lattice. 

An important example that demonstrates the potential of PM spectroscopy is shown in Fig. 22.6 for a trans-(CH), film (d 1000 A) kept at 210 K [18]. Due to the ID character of (CH), the photoinduced soliton bands are sharply defined. Two well-defined bands, one PA band and one PB band, are seen, and the sum rule for Aa [Eq. (11)] is approximately obeyed. This also shows that the two bands share a common origin. The additional modulation around the PB peak is probably caused by vibronic side bands, and we identify the shoulder at 1.4 eV as the zero-phonon transition. Associated with the PA band 8S ), which peaks at 0.5 eV at this temperature, is a narrow photoinduced IR-active vibration at 0.17 eV [41,42], which shows that the PA band is due to photoinduced charged defects S ). A sharp feature in the PB band that could be associated with the... 

In Ref. [4], the soliton lattice configuration and energy within the SSH model were found numerically. Analytical expressions for these quantities can be obtained in the weak-coupling limit, when the gap 2A() is much smaller than the width of the re-electron band 4/0. At this point it is useful to define the lattice correlation length ... 

The electronic band structure of a neutral polyacetylene is characterized by an empty band gap, like in other intrinsic semiconductors. Defect sites (solitons, polarons, bipolarons) can be regarded as electronic states within the band gap. The conduction in low-doped poly acetylene is attributed mainly to the transport of solitons within and between chains, as described by the intersoliton-hopping model (IHM) . Polarons and bipolarons are important charge carriers at higher doping levels and with polymers other than polyacetylene. 

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