Physics – Condensed Matter – Materials Science
Scientific paper
1994-02-21
Phys. Rev. B 48 (1993) 2515-2528
Physics
Condensed Matter
Materials Science
36 pages, Latex
Scientific paper
10.1103/PhysRevB.48.2515
We analytically study phonon transmission and localization in random superlattices by using a Green's function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice structure factor. This is done by considering the backscattering of phonons, due to the complex mass density fluctuations, which incorporates all of the forward scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.
Nishiguchi Norihiko
Nori Franco
Tamura Shin-ichiro
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