Polaron-exciton levels

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.

Figure 22.4c. Following the same arguments given previously for polaron transitions, we expect three strong transitions, PP1-PP3. For a loosely bound PP, these transitions are not far from transitions P1-P3 of polarons. However, for a tightly bound PP excitations, we expect a single transition, PP2 to dominate the spectrum, as PPi is considered to be intraband with traditional low intensity and PP3 is close to the fundamental transition and therefore difficult to observe. In this case, there are mainly two states in the gap, and the excitation is also known as a neutral BP (BP ) or a polaronic exciton. However, the PP2 transition is close in spirit to transition X2 discussed above for excitons, as a second electron is also promoted to the excited level in the case of PP. Then from the experimental point of view, it is not easy to identify and separate the transitions of a trapped exciton (2ft) from those of a tightly bound PP of (BP ) in the PM spectra. However, they may differ in their PADMR spectra [63].

Fig. 3, Schematic picture of the different processes occurring in B850 at low temperature excitation into the B850 band creates an initial, nonselective population on exciton levels (1) this population relaxes through the exciton band in about 100 fs (2) the lowest exciton states are mixed with charge-transfer states and these states are populated by means of a slower process occurring within 0.6 ps (3) due to polaron formation, slow motion along the relaxation coordinate takes place on a time scale of about 10 ps (4) stimulated emission from the polaron states is seen as a new band in the red part of TAS (5). At room temperature, thermal excitations do not allow population of charge-transfer states for a sufficient time to relax the population along the relaxation coordinate hence, only stimulated emission from the lowest exciton states is observed (6).

For the reflection symmetric two-level electron-phonon models with linear coupling to one phonon mode (exciton, dimer) Shore et al. [4] introduced variational wave function in a form of linear combination of the harmonic oscillator wave functions related with two levels. Two asymmetric minima of elfective polaron potential turn coupled by a variational parameter (VP) respecting its anharmonism by assuming two-center variational phonon wave function. This approach was shown to yield the lowest ground state energy for the two-level models [4,5]. 

For our formal treatment of the fermionic 2-level system we assume that we may describe the behaviour of electrons in the one-electron approximation. Then each electron is represented by a wave function that is independent of the wave functions of other electrons, and the individual wave functions may be linearly superimposed. This picture often proves useful in the context of inorganic semiconductors [2,3]. However, it may be highly questionable in organic and molecular matter, where excitonic [4] and polaronic effects are often predominant [5]. 

These experiments yield an exciton binding energy of 0.5 eV relative to separate electron and hole. This is a large value. An important consequence, although one that is never mentioned, is that in such a case, the polaron binding energy u>p (see Fig. 7 of Chapter 11) must be larger than 0.25 eV for the absorption between polaron levels in the gap to occur below that of the exciton in practice, the polaron absorption, if it exists, will remain hidden under the excitonic absorption. 

When EB is protonated leading to ES, a continuous shift of the exciton band from 2 to 1.5 eV is observed, together with the growth of the polaron band, due to the formation of within-gap new defects levels. The polaron state with unpaired spin, (that is to say the isolated polaron) has been determined by Electron Spin Resonance at 2.75 eV when the level of protonation increases up to the formation of two associated polarons, the spin resonance disappears, while the peak shifts up to 3.1 eV [51]. In ES, beside the polaron lattice peak at (on an average) 2.9 eV, a new absorption centred at 1.0 eV attributed to intrachain ffee-carrier excitation appears also [52]. The near-UV absorption weakens, since the metallic character of ES is inconsistent with the keeping of a 7t —> tt transition. 

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