Wannier-like excitons

To summarize, we have demonstrated the possibility of strong resonance hybridization of ID Frenkel and Wannier-Mott excitons in parallel organic and semiconductor wires. Like the 2D case, the new states possess the properties of both types of excitons. They have a relatively large size (along the wires) like Wannier-Mott excitons, but they also have a large transition dipole moment which is typical for Frenkel excitons. Thus, one may expect the same as for 2D structures (see Fig. 13.1b) the strong nonlinear optical effects in such structures. 

Figure 3a shows several representative photoconductivity excitation spectra in pure xenon Fig. 3b for argon doped by ethane. In pure liquid and solid xenon and krypton, the value of as determined by means of the photoconductivity threshold is in full accord with its value as found from the limit of Wannier-Mott excitonic series (Asaf and Stelnberger, 1974 Laporte et al., 1985 see also below). This fact furnishes independent support for the applicability of solid-state concepts like energy... 

It should be stressed that EM itself does not work directly with CMOs, but proposed in this section algorithm allows to recover from this condition and to obtain CMOs omitting numerous iterative diagonalization procedures. And it is of great importance to have the CMOs to be able to describe delocalized phenomena, like band structure, low frequency vibrational modes such as lattice vibration, Wannier type excitons etc. 

Thus, Mott-Wannier excitons can give rise to a number of absorption peaks in the pre-edge spectral region according to the different states = 1, 2, 3,... As a relevant example. Figure 4.14 shows the low-temperature absorption spectrum of cuprous oxide, CU2O, where some of those hydrogen-like peaks of the excitons are clearly observed. These peaks correspond to different excitons states denoted by the quantum numbers = 2, 3, 4, and 5. 

Whereas the Frenkel tight-binding description is valid for excitons localized to atomic dimensions, the Wannier approximation describes excitons delocalized over many lattice distances. The hydrogen-like wave functions associated with these states serve as envelope functions describing average probability in spatial regions of lattice-constant dimensions. 

The localization of the lowest-energy exciton in ionic solids like the alkali halides is such that neither the Frenkel nor Wannier approximation is valid. An early picture of the excitation by Hilsch and Pohl [58] was that absorption of a photon results in the transfer of an electron from one of the halogen ions to a neighboring alkali ion. This charge-transfer model of the exciton attributed observed double-absorption peaks to the spin-orbit splitting of the halide ion, and successfully predicted exciton energies by the empirical relation... 

An early discussion of the theoretical problem of Mott-Wannier excitons in liquids was given by Rice and Jortner (1967). We recall that these excitons can be regarded as non-localized electron-hole pairs held together by their Coulomb interactions weakened by the polarization of the medium. The Mott-Wannier exciton peaks, E, are usually not related to any atomic excitations, and their positions are given by the hydrogen-like formula... 

---