Polaron formation

So far, electrochemical measurements have not provided any direct proof for the formation of a bipolaron state in oligbmers or polymers which is significantly more stable than the polaron state. In general, in terms of energy the redox potentials E° for bipolaron formation should be much lower than the potentials Ej for polaron formation (/E / < /E /). However, more recent electrochemical and ESR spectroscopic studies by Nechtschein et al. indicate that the bipolaron state is not much more stable than the polaron state... 

Bussmann-Holder A, Keller H, Muller KA (2005) Evidences for Polaron Formation in Cuprates 114 367-386... 

Many other time parameters actually enter - if the molecule is conducting through a polaron type mechanism (that is, if the gap has become small enough that polarization changes in geometry actually occur as the electron is transmitted), then one worries about the time associated with polaron formation and polaron transport. Other times that could enter would include frequencies of excitation, if photo processes are being thought of, and various times associated with polaron theory. This is a poorly developed part of the area of molecular transport, but one that is conceptually important. 

The Seebeck coefficient a becomes temperature-independent only above a temperature Tt, where T, — 300 K for x < 0.1 In magnetite, T, can be identified with the onset of strong electron-phonon coupling. The temperature-independent a shows a continuous evolution from the value for P = 1 described by Eq. (16) at x = 0.1 to that by Eq. (15) for x > 0.8. Although small-polaron formation is observed for x > 0.2, regions apparently persist where multielectron jumps can occur. 

The formation and transport properties of a large polaron in DNA are discussed in detail by Conwell in a separate chapter of this volume. Further information about the competition of quantum charge delocalization and their localization due to solvation forces can be found in Sect. 10.1. In Sect. 10.1 we also compare a theoretical description of localization/delocalization processes with an approach used to study large polaron formation. Here we focus on the theoretical framework appropriate for analysis of the influence of solvent polarization on charge transport. A convenient method to treat this effect is based on the combination of a tight-binding model for electronic motion and linear response theory for polarization of the water surroundings. To be more specific, let us consider a sequence... 

Fig. 5 Polaron configuration vs. time, i.e., polaron formation, for zero field (From Rakhmanova and Conwell [65])...

Interaction of electrons with phonons, and the fact that the presence of a trapped electron can deform the surrounding material, allows the radius of an empty localized state to change when the state is occupied. Also, in a condensed electron gas phonons lead to a mass enhancement near the Fermi energy, or in some circumstances to polaron formation. For the development of the theory, and comparison with experiment, it is therefore desirable to begin by choosing a system where these effects are unimportant. The study of doped semiconductors provides such a system. This is because the radius aH of a donor is given, apart from central cell corrections, by the hydrogen-like formula... 

There are several papers on the energy-band structure of SrTi03, e.g. Soules et al, (1972). Wolfram (1972) emphasized the two-dimensional character of the Ti d-band (the conduction band), giving a rapid rise of N( ) with . This will facilitate polaron formation. 

It is of course possible that a carrier in the conduction band or a hole in the valence band will form a spin polaron, giving considerable mass enhancement. The arguments of Chapter 3, Section 4 suggest that the effective mass of a spin polaron will depend little on whether the spins are ordered or disordered (as they are above the Neel temperature TN). This may perhaps be a clue to why the gap is little affected when T passes through TN. If the gap is U —%Bt -f B2 and Bt and B2 are small because of polaron formation and little affected by spin disorder, the insensitivity of the gap to spin disorder is to be expected. 

We think that all these observations are to be explained by the assumption that metallic V203 is a highly correlated electron gas, as first suggested by Brinkman and Rice (1970b) and described in Chapter 4. The very low degeneracy temperature suggests that there may also be some mass enhancement of the carriers by polaron formation. Two electrons per atom would just half fill an ej band, so that the number of electron-like and hole-like carriers would be... 

In the case discussed here a Mott transition is unlikely the Hubbard U deduced from the Neel temperature is not relevant if the carriers are in the s-p oxygen band, but if the carriers have their mass enhanced by spin-polaron formation then the condition B U for a Mott transition seems improbable. In those materials no compensation is expected. We suppose, then, that the metallic behaviour does not occur until the impurity band has merged with the valence band. The transition will then be of Anderson type, occurring when the random potential resulting from the dopants is no longer sufficient to produce localization at the Fermi energy. 

Fig. 1. Three THz-scans at 10K The pulse transmitted through air (Efree(tJ), the unexcited sample (E,ram(t)), and the photoexcited sample ( , (/)). The 45ps delay between and E,rani is caused by the large real part of the dielectric function (see inset of Fig. 2). A less obvious phase shift also exists between E,mns and associated with the real part of e. Inset Left - the (001) face of rutile. Right - the lattice distortion when an electron is placed in the polar lattice results in polaron formation (partly) positively charged Ti-atoms are attracted, and (partly) negative O-atoms repelled (see text).

In most organic semiconductors the presence of charges modifies the local structure of the network by deformation of the particular site. This so-called polaron formation thus creates scattering centres for other charges. Moreover these locally trapped carriers commonly alter the energy conditions because of their Coulomb interaction. In combination with the polaron energy, the latter may be attractive or repulsive. These effects, as they involve more than one electron, force us to give up the one-electron picture and hence to use the correlated-electron description. 

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