Dynamics of a Mosaic of Quasicrystals from Two Lattices When One Lattice Slides Over the Other

Abstract

The discontinuous dynamics of a quasicrystalline mosaic consisting of two hexagonal or square lattices rotated by 90° relative to each other, where one lattice undergoes uniform translational motion, is considered. It is shown that small displacements of this lattice can lead to large jumps of the mosaic center to the “node” positions of the initially stationary quasicrystalline mosaic, resulting in intermittent jumps despite the uniform slow sliding of one lattice over another. Such lattice sliding in quasicrystals formed by 2D atomic layers, photonic and phononic crystals—with their weak interlayer bonding—makes it possible to use the considered effect in various applications of elements involving finite-sized quasicrystalline structures. It is also noted that, for unidirectional motion of the movable lattice, mosaic jumps can occur at discrete instants not only in the direction of its motion but also in the opposite direction. When the mosaic jumps within a quasicrystalline sample, the symmetry and arrangement of mosaic tiles are disrupted, which changes its physical dispersion properties during jumps and is expected to lead to pulsed behavior of the corresponding electronic, photonic and phononic characteristics of the sample.