Polaron energy levels

Figure 7-23. Schematic diagram of energy levels and optical irunsiciits of neutral molecule, polaron (P+) and bipolar. HP2+).

Kigurc 7-35. Comparison of the energy levels and optical transitions of oppositely-charged polarons and polaron pairs. 

Fig. 4. Energy level diagrams showing possible electronic configurations for positively-charged polaron (a) and bipolaron (b) defects and (c) a schematic bipolaron band model. The negatively-charged polaron would carry three electrons and the bipolaron four. Also shown is the neutral polaron-exciton (d) which would decay to restore the chain structure.

Fig. 1.13. Energy levels of a pair of polarons in singlet and triplet states in a magnetic field. If 2J = 0, the triplet sublevel ms = 0 will degenerate with the singlet state and can be (de-)populated via intersystem crossing...

If two polarons of like sign are formed close to each other, a bipolaron is formed. Two energy levels are created by a bipolaron in the bandgap. They are both occupied either by two electrons (for a negative bipolaron) or by two holes, i.e. they are empty (in the case of a positive bipolaron). The bipolaron has no spin. The bipolaron may not be stable because of the repulsion of the two polarons which constitute the bipolaron. However the dopant ions in the neighborhood stabilize the bipolaron. 

Optical Signatures of Solitons, Polarons, and Bipolarons The formation of these excitations generates energy levels corresponding to optical transitions below the fundamental absorption that between the valence and the conduction band in one-electron models (but see Section... 

Fig. 9.12 Energy level schemes of solitons and polarons in polyacetylene (a) soliton, (b) anti-soliton, (c) negative soliton, (d) positive soliton, (e) negative polaron and (f) positive polaron.

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. 

Transformation. The transformation of the Hamiltonian (2.1) which yields a weak residual excitation-phonon coupling even when the g are large has been discussed several times (4, 7, 16, 17). It prSduces a uniform shift in the excitation energy levels and a displacement in the equilibrium position of the phonons corresponding to the formation of a polaron. Since the transfer interactions J compete with this tendency to form a localized... 

In polythiophene and in the substituted polythiophenes, polarons were identified [135-137]. The data was analyzed using the amplitude mode and phase mode model, yielding an approximate value of 0.3 for the pinning parameter, for both the photoinduced and doping induced polarons (the IRAV appear at nearly the same frequencies). The larger pinning, relative to polyacetylene, is possibly related to the different electronic energy level structure of the polarons. 

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