Self-consistent potential of intrinsic localized modes: Application to diatomic chain

A mean-field theory of intrinsic localized modes (ILMs) in anharmonic lattices is proposed, which allows one to perform calculations for macroscopically large lattices of arbitrary dimensions with realistic pair potentials. In the theory, the original nonlinear problem is reduced to a linear problem of mode localization on the self-consistent harmonic local potential. This enables us to apply the Lifshitz method of the perturbed local dynamics of phonons for the calculations of ILMs. In order to check the theory, the characteristics of the ILMs in a diatomic chain with the Born-Mayer-Coulomb pair potential are found and compared with the corresponding molecular-dynamics simulations. The results of both considerations are in a very good agreement.

Figure 1

The dependence of $\gamma$ on the dimensionless amplitude $a$ for the Toda, Morse, and Born-Mayer-Coulomb potentials (in the $P∕{\rho }^2$ units). For the Morse potential, $a=2\overline{A}∕\rho$, while for the Toda and for the Born-Mayer-Coulomb potentials, $a=\overline{A}∕\rho$; for the latter potential, $\rho ∕d=0.1117$ (the value of this parameter in NaBr).

Figure 2

The dependence of the dimensionless frequency $\omega ∕{\omega }_m$ of an odd ILM on the amplitude $A_0$ (in Å) of the central atom (Na) in a NaBr-type diatomic chain; ${\omega }_m$ is the top phonon frequency, ${\omega }_o$ is the bottom of the optical band, and ${\omega }_a$ is the top of the acoustic band.