Die Kunst of Phonons: Lectures from the Winter School of by George K. Horton, E. Roger Cowley (auth.), Tadeusz

By George K. Horton, E. Roger Cowley (auth.), Tadeusz Paszkiewicz, Krzysztof Rapcewicz (eds.)

Phonons: General: fresh development in utilizing the potent power approach (G.K. Horton, E.R. Cowley). Momentum and Quasimomentum within the Physics of Condensed subject (A. Thellung). Phonon Focusing: Phonon Imaging at Ultrasonic Frequencies (A.G. Every). Nonequilibrium Phonons: Timedependent particular warmth of Crystals and Glasses at Low Temperatures (N.S.M. Meissner). Interaction of Bulk Phonons with Low Dimensional Gases of Carriers: Acoustic Phonon interplay with Twodimensional Electron and gap structures (L.J. Challis, A.J. Kent). Phonon Mediated Detectors of basic Particles: program of Phonon Physics to Cryogenic Detectors (H. Kraus). Molecular Crystals: Phonon Scattering and warmth move in easy Molecular Crystals (V.G. Manzhelii, V.A. Konstantinov). Electron Systems: the outside Impedance and the Slab Conductivity of Metals past the comfort Time Approximation Transition (J. Czerwonko et al.). 28 extra articles. Index.

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2) in the equivalent form [2Wn + 2p k + I;p(w+) - I;p(w_ ]q,ppl = ~Gp (15PPI + l: Wpp" q,PIIPI) , (3) (0"=0,1), (4) pp" where ~Gp = Gt+(w+) - G;jw_). In the dipole approximation (d. Ref. 4) we can write l: q,ppl = 27ri ~Gp/w (q,o + 3p q,lk/w) , q,,,=q,,,(k,w,n), pi where w = [w 2 - ~o(w)11/2, k = k/lkl. and I;o (w + iO) = ~o(w) - ifo(w) is the momentum independent self-energy calculated by ignoring interference effects 3 (see also expression (12) below. From (3) we then find the algebraic system of equations -w n q,o + k q,l = -iw/47r , (5') (5") where M = f(w) + 37rw-3 l: ppl ~Gp (p k) Wppl ~Gpl (p' k) (6) is the memory function.

Taking into consideration only the central interaction between atoms, we use the magnitudes of the force constants calculated on the basis of the data published in the Ref. [12]. The obtained results are shown in Figs. 7-10. Fig. 7. presents the functions v(w) = 2wg(w 2) for the layer CU02 in two different cases: i) curve (a) corresponds to the simplified model, considered in preceding section; ii) curve (b) corresponds to the model taking into account all the atomic interactions ~ Cu 2 2 -VCu 1 2 "cu2 y ~ \I~u1 /\..

It is known that the phonon density of a 2D dispersion law has logarithmic van Hove singularities [1,2] at the squared frequencies w~ and w; ~ Am - w~. Let us investigate the change of the spectral densities PL(A), PII(A) and the total squared frequency distribution function g( A) of the layered crystal caused by increasing the anisotropy of the interatomic interaction (Fig. 1). 1) the function g(A) has a form that is typical for crystals with an isotropic interatomic interaction. The centre of gravity of the spectral density P1.

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