Dispersive corrections to continuum elastic theory in cubic crystals

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Abstract
Recent experiments using ballistic phonon imaging have provided very accurate pictures of acoustic-phonon dispersion for GaAs in the frequency range 0.1–1 THz. This work has been previously analyzed using microscopic lattice-dynamics models. An alternative description of this phenomenon which is natural, compact, and simple is provided by continuum elasticity theory with dispersive corrections included, as developed in the present paper. Previous models and experiments are successfully analyzed by the present theory. It is shown that the reason for the failure of many earlier models to match experiment is that they impart insufficient dispersion to the transverse acoustic branches. A single additional parameter contained in the dispersive elastic model appears to control the important features of the dispersion of these branches; six other parameters permitted by symmetry do not appear crucial. We show that the present dispersive elastic model can be derived as a rigorous limit of microscopic lattice-dynamical theory. The elastic model illuminates simple relationships between the phonon-imaging experiments and other physical phenomena, e.g., specific heat and ultrasound.