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Energy Renormalization and Damping of Long‐Wavelength Phonons in Amorphous Solids
Author(s) -
Handrich K.,
Öttking R.
Publication year - 2001
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200106)225:2<289::aid-pssb289>3.0.co;2-w
Subject(s) - phonon , condensed matter physics , physics , magnon , renormalization , amorphous solid , wavelength , ferromagnetism , quantum mechanics , chemistry , organic chemistry
We consider the energy renormalization and damping of long‐wavelength phonons in monatomic amorphous solids within the harmonic approximation due to the influence of long‐range structure fluctuations. By employing a formalism analogous to the Matsubara‐Kaneyoshi fomalism (MKF) established for amorphous ferromagnets we derive the structure averaged Green's function 〈 G qq ′ ( E )〉 which contains the phonon self‐energy in “improved quasi‐crystalline approximation” as a start approximation in the equation of motion for the Green's function, thus containing important structural information already. The typical static structure factor in the small‐angle region is approximated by convenient analytical model functions. We then derive the damping and the sound velocity renormalization for long‐wavelength longitudinal and transverse acoustic phonons, where the former is found to show a characteristic q 4 behavior in the small‐ q range (phonon Rayleigh scattering) due to the density fluctuations acting as “point defects” for extremely long‐wavelength phonons, while in the larger‐ q range a q 2 law is found. The renormalization R ( q ) shows generally uniform behavior for all model functions used for the static structure factor. Extrapolation of the renormalized energy from the larger‐ q region provides an apparent gap energy induced by the amorphous structure, which can be explained by the nascency of “compensational phonons” which accompany the phonon compensating the inhomogeneities, thus forming a “phonon‐dressed phonon”. The mentioned features of long‐wavelength phonons in amorphous solids show wide similarities to long‐wavelength magnons in amorphous ferromagnets.