Polaron conduction

Webb JB, Sayer M, and Mansingh A. Polaronic conduction in lanthanum strontium chromite. Can. J. Phys. 1977 55 1725-1731. 

At higher temperatures, 700-1000 K, a positive thermoelectric power a(T) is essentially temperature-independent and the evolution of its magnitude with S is consistent with polaronic conduction described by the statistical component... 

D. Polaronic Conductivity Along a Hydrogen-Bonded Chain... 

As we pointed out above, not only the low-frequency mode (99 cm-1), but also the high-frequency mode (756 cm-1), is involved in the protonic conductivity. The criterion for the low-frequency polaronic conductivity is the inequality Ha> < 2kBT, where go is the frequency of the phonons co = 99 cm 1 falls under the inequality at T > 50 K. At the inequality ha > 2kBT, which holds true for the mode with a frequency of 756 cm-1, the standard model of the mobility of the small is not valid therefore, this case should be treated separately. 

During the polaron transport therefore, this polaron formation energy behaves as an additional barrier for hopping. Thus the polaronic conductivity, due to the carriers which are excited above the mobility edge, is given by. 

Although the single polaron problem was one of the early subjects of interest for condensed matter physics, polaronic conduction at a finite density remains a complex and poorly understood topic even these days, with many open questions. The organic single-crystal OFETs represent a unique tool to address these questions in a class of materials relevant for the emerging field of plastic electronics. 

Polarization of the lattice results in a reduction of the energy of the system, and the carrier is then assumed to be localized in a potential energy well of effective depth Eg- It follows that for migration to occur, the carrier has to be supplied with at least that much energy, and consequently the mobility becomes thermally activated. It can be shown (see Prob. 1.2c) that polaron conductivity can be described by an expression very similar to that for FICs, that is,... 

It can be seen from the alternative resonance form where the charge and spin are placed on the other set of nitrogen atoms that the overall structure is expected to have extensive spin and charge delocalization resulting in a half-filled polaron conduction band. 

Moreover, Eq. (5.1) assumes that conduction in each energy shell can be treated separately. This is a doubtful procedure when charge motion involves exchange of energy with the lattice as in the case in phonon assisted hopping and polaron conduction. 

The ionic contribution is small. Polaron conduction and predominant optical-mode scattering are assumed... 

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