Phonons optical, bound states

The study of bound states of optical phonons or, stated more generally, the study of the effects of strong anharmonicity in the vibrational spectra of crystals, has grown out of the development of modern solid-state physics and to no less extent, it was motivated by the requirements of experiment. 

To illustrate the kind of useful information that can be obtained, we consider here in some detail one example—calculation of the optical phonon-phonon interactions in diamond. This will serve both to illustrate the power of the method and to shed some light into the phenomenon of two-phonon Raman anomaly in diamond. It was observed that the two-phonon Raman spectrum of diamond has an anomalous sharp peak (not seen for Si and Ge) at 2667 cm which is at an energy 3 cm higher than twice the optical phonon frequencies at r. Despite a number of theoretical works, the nature and origin of this peak is still a mystery. One particularly intriguing explanation was the two-phonon bound state theory by Cohen and Ruvalds. They proposed that a two-phonon bound state is formed... 

For the purpose of understanding the two-phonon bound state problem, we are interested in the k 0 phonons and their interactions. We, therefore, need to calculate x° X 1 XX X X" where A denotes the various optical modes. For example, °X X" gives the amplitude for the process... 

This work contributed in two major ways. First, the calculation shows that it is now possible for the first time to calculate from first principles phonon-phonon interaction parameters that are inaccessible from experiment. Second, since all the effective four-phonon terms (direct plus mediated processes up to are attractive for the k = 0 optical phonons in diamond, the formation of the two-phonon bound state is unlikely in this system. 

The X-ray excitation process frequently is analyzed in terms of an excitonic electron hole pair (e.g. Cauchois and Mott 1949). The excitonic approach to X-ray absorption spectra accounts for the fact that the excited state is a hydrogen-like bound state. The X-ray exciton is different from the well-known optical excitons. In the latter cases the ejected electron polarizes a macroscopic fraction of the crystal-fine volume because the lifetime of optical excitations is in the order of lO s. The lifetime of the excited deep core level state, however, is in the order of 10 — 10 s, much too short to p-obe more than the direct vicinity of excited atom. Following Haken and Schottky (1958) the distance r between the ejected electron and core hole of an excited atom for E = 1 turns out to be r oc [h/(2m 0))] Here m denotes the effective mass of the ejected electron, to is the phonon frequency and is the dielectric constant. A numerical estimate yields r 10 A. Thus the information obtainable in an L, spectrum of the solid is very local the measurement probes essentially the 5d state of the absorbing atom as modified from the atomic 5d states by its immediate neighbors only. It is not suited to give information about extended Bloch states. On the other hand it is well suited to extract information about local correlations within the 5d conduction electrons, whose proper treatment is at the heart of the difficulty of the theory of narrow band materials and about chemical binding effects. 

In a non-exhaustive literature search, a brief account is given here on the study of phonon and its vibrations. Corso et al. did an extensive study of density functional perturbation theory for lattice dynamics calculations in a variety of materials including ferroelectrics [93]. They employed a nonlinear approach to mainly evaluate the exchange and correlation energy, which were related to the non-linear optical susceptibility of a material at low frequency [94], The phonon dispersion relation of ferroelectrics was also studied extensively by Ghosez et al. [95, 96] these data were, however, related more with the structure and metal-oxygen bonds rather than domain vibrations or soliton motion. In a very interesting work, a second peak in the Raman spectra was interpreted by Cohen and Ruvalds [97] as evidence for the existence of bound state of the two phonon system and the repulsive anharmonic phonon-phonon interaction which splits the bound state off the phonon continuum was estimated for diamond. 

The direct proof that H is present in certain centers in Ge came from the substitution of D for H, resulting in an isotopic energy shift in the optical transition lines. The main technique for unraveling the nature of these defects, which are so few in number, is high-resolution photothermal ionization spectroscopy, where IR photons from an FTIR spectrometer excite carriers from the ls-like ground state to bound excited states. Phonons are used to complete the transitions from the excited states to the nearest band edge. The transitions are then detected as a photocurrent. 

It would be desirable to obtain symmetry information on V2H. All efforts to generate optical spectra of ground-to-bound excited state hole transitions have failed so far. Because of the low concentration of V2H, we attempted to use PTIS. This technique works well if the bound excited state lifetimes are long so that a phonon can interact with the bound hole... 

Let us now consider what is the analog of a Fermi resonance in a molecule when we consider the crystals. In going over from an isolated molecule to a crystal, the branches of optical phonons appear. In the region of overtone and sum frequencies, several bands of many-particle states arise and, if anharmonicity is sufficiently strong, bands of states with quasiparticles bound to one another (for instance, biphonons) will also appear. Thus, in crystals a large number of... 

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