Collective oscillations of twin boundaries in high-temperature superconductors as an acoustic analogue of two-dimensional plasmons

Low-frequency collective oscillations in a superlattice consisting of alternating highly anisotropic layers are considered. Such superstructure may be formed in the ferroelastic near the structural phase transition by alternation of twins. For the surface waves, propagating along the layers, the conditions and the range of existence of those with the dispersion law {ω}{~}k1/2, characteristic for two-dimensional plasmons, have been analyzed for a solid-state system with consideration for elastic anisotropy and retardation of acoustic waves. Such excitations (``dyadons'') were used by Horovitz, Barsch, and Krumhansl [Phys. Rev. B 36, 8895 (1987)] in an attempt to explain the anomalies of low-temperature thermodynamic and kinetic characteristics of high-Tc superconductors. We have shown that the similarity of the densities of the matching phases and the retardation of elastic waves in the crystal narrow the range of existence of dyadons, but the high elastic anisotropy of the solid phases enlarges the range of existence of such excitations in solid-state systems. An example of possible crystalline geometry of the phase matching, for which there arise collective excitations of the type under consideration, is found. For transverse and longitudinal waves propagating across the layers, the existence is proved of low-frequency acoustic branches separated by a wide gap from the nearest optical branches.