Strongly localized anharmonic modes in perfect and imperfect crystals

TL;DR

This paper introduces an efficient method for analyzing strongly localized anharmonic vibrational modes in perfect and impure crystals, combining analytical and numerical approaches to reveal directional dependencies at large amplitudes.

Contribution

It presents a novel method reducing nonlinear lattice problems to linear inverse scattering problems, enabling detailed analysis of localized anharmonic modes in crystals.

Findings

Localized modes depend strongly on crystallographic directions at large amplitudes.

Numerical calculations show significant amplitude effects in impurity-laden alkali halide crystals.

Analytical descriptions are provided for monatomic chain localized modes.

Abstract

Localized modes of large amplitudes in nonlinear lattices are considered. The applied method allows the reduction of nonlinear problem to a linear inverse problem of phonons scattering on a local potential. The method is efficient in the case of strongly localized modes. Analytical description of such modes in monatomic chain is given. Results of numerical calculations of anharmonic local vibrations of light ions in pure and impure alkali halide crystal are presented. It is found that, in the case of amplitudes ~0.5A, the vibrations depend very strongly on the crystallographic directions.