Excitons two-dimensional

Note that for > 0 and e2 > 0 the fluorescent photons can propagate in both half-spaces. If one of the values of e , e.g. e2(wo), is negative, then the fluorescent photons can propagate in the half-space z > 0 only. In this case alongside the enormous width of the two-dimensional exciton with fc = 0a shift of its energy occurs as well. In fact, for this case (12.29) yields... 

These relations generalized results obtained in (37) (see also Ch. 3) for the case of two-dimensional excitons in the vacuum and demonstrate the dependence of the quantity T on the refractive indices of the contacting media. They show, for example, that when the frequency ujn tends to the frequency of the bulk dipole resonance (in this case e2( o) can be large) the radiation width r should decrease within the scope of the microscopic theory this problem was discussed by Tovstenko (38). Unlike the radiation width T, which under the indicated conditions is much larger than To, the shift <5 is usually of the order of, or smaller than the shift of the exciton energy due to the exciton-phonon interaction. For this reason the radiative shift generally plays a minor role. 

The general Lifshitz theory was applied for two-dimensional excitons and polaritons in an organic microcavity by Litinskaia (28). Unfortunately, we are not able to go in details of these calculations here. Note only that also stud-... 

Since in quantum wells electrons and holes can freely move only within the quantum well plane, bound electron-hole states, i.e. excitons, become two-dimensional in nature as well. The exciton binding energy is enhanced four-fold in the ideal two-dimensional case compared to a conventional three-dimensional case. In addition, the exciton oscillator strength is also enhanced. In the optical spectra, this leads to pronounced excitonic features which are usually observed even at room temperature. 

Two-Dimensional Coherent Infrared Spectroscopy of Vibrational Excitons in Peptides... 

The situation is somewhat more complicated in two-dimensional polysilanes, which have intermediate properties between the one-dimensional chain-like polysilanes and three-dimensional bulk silicon. The gap is of a quasi-direct nature as the indirect gap is only slightly smaller than the direct one [11]. However, the excitons strongly bind to the lattice which results in a large Stokes shift of the PL [26]. The observed blue shift of the absorption and photoluminescence with decreasing size of the polysilanes is considered to be due to confinement effects of the excitons [12,26]. The strong coupling of the exciton to the lattice decreases somewhat the blue shifts as compared with the linear chains, and it results in a stronger localization of the exciton over a smaller number of Si atoms [12,26]. 

Up to this point we have considered the influence of retardation on the form of exciton bands in three-dimensional crystals. Examination of excitons in two-and one-dimensional crystals, to which we devote this section, is also of interest, since we observe a number of important and specific phenomena. As an aside we notice that the examination of exciton spectra from one- and two-dimensional crystals is important from the point of view of possible applications (quantum wells, quantum wires, polymers, etc.). Below we follow the paper (21).43... 

An entirely analogous procedure can be applied to determine the radiative width of exciton states in two-dimensional molecular crystals. In this case an exciton can decay only into a photon, which has an in-plane component of the wavevector equal to the exciton wavevector. Denote this component by ky, and the component perpendicular to the crystal plane by q (q = ky + qj ). Then the probability of decay of an exciton with given wavevector k is equal to... 

Quite analogously we can consider retardation effects in two-dimensional crystals. In this case the excitonic dispersion rule has the form... 

Fig. 4.5. Excitonic dispersion in two-dimensional crystals with retardation.

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