Localized moving breathers in a 2D hexagonal lattice

Abstract

We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2-D hexagonal non-linear lattice. The lattice is subject to an on-site potential in addition to longitudinal nonlinear inter-particle interactions. This study investigates the prediction that stable breather-like solitons could be formed as a result of energetic scattering events in a given layered crystal and would propagate in atomic-chain directions in certain atomic planes. This prediction arose from a long-term study of previously unexplained dark lines in natural crystals of muscovite mica.63.20.Pw, 63.20.Ry, 03.40.Kf.The response of a nonlinear 2D atomic lattice when embedded in a surrounding 3D lattice is presently of much interest in connection with transport phenomena in layered crystals. Two examples of such crystals are the copper-oxide based high temperature superconductors and the potassium based silicate muscovite mica. Fortunately the optical transparency of the latter allows the study of energetic events at the atomic level. This is possible in mica because of tracks made visible by impurities of transient defects, through triggered solid-state phase transitions. A study of these tracks arising from nuclear scattering events led to the suggestion that energy could be transported over large distances through the crystal by some sort of energetic intrinsic localized mode (ILM) on the lattice [1]. The interesting and novel aspect of this prediction was that these ILMs would travel along the crystal axes and remain localized in both longitudinal and transverse directions with little or no lateral spreading. This is despite the fact that the 2D lattice has full hexagonal symmetry. This one-dimensional behavior in a two-dimensional lattice was called quasi-onedimensional (QOD) and the resulting ILMs were called "quodons" [2].The purpose of this present letter is to demonstrate numerical simulations of a mica-like model which support the QOD conjecture. Our intention is not to provide a detailed model of the mica system at this stage, but merely to present a simplified model which maintains much of the overall qualitative features of the mica system and yet can be easily studied. The model is general enough to suggest the possibility of QOD effects in other hexagonal crystal structures, and even other geometries such as square lattices.Muscovite mica has a layered structure. A conspicuous feature of this structure is the mono-atomic planes of *

Breathers in cuprate-like lattices

“…This was motivated by a previous study [17], where the superconducting properties of cuprates were correlated to the existence of linear chains of atoms, which were conjectured to transport one-dimensional nonlinear waves. Our results provide a realization of these waves in the form of mobile discrete breathers, which we have already established in the hexagonal lattice case [13].…”

“…Radiation to the adjacent chains of atoms is, in principle, to be expected. Nevertheless, we recently found that moving breathers can exist in hexagonal 2D lattices, and showed that they show a remarkable transverse focusing effect [13].…”

2-D Breathers and Applications

“…Note that these fixed oxygens are really off the plane, so that the distances to the K atoms are computed in full 3D Euclidean space (the z-coordinate being constant). This is in contrast with our initial model in [14], where we placed 6 fixed atoms in the plane, interacting through a Morse potential. Using the intuition gained about discrete breathers in 1D models, it was judged that it was not the particular shape of the nonlinear potentials used which was of main importance.…”

“…In [14] we showed for the first time how localized excitations of longitudinal type can move in a 2-D lattice. These lattice modes appear to be the mobile version of intrinsic localized modes [24], more commonly known as discrete breathers.…”

“…For the problem of mica, we are now trying to introduce the most realistic potentials we can find [4] and check whether the combination of on-site and inter-atomic forces for the K atoms allow for moving breathers. Our initial studies including only short range forces suggest so [13]. It is now needed to study the effect of long-range Coulombic forces on these moving solutions, which is not well known even for 1D models.…”