LOCALIZED PHONONS IN HEXAGONAL 2D CRYSTALS

AT THEIR DIFFERENT TYPES OF SOLITONS

M. Belhadi1, R. Tigrine1,2*, M. Bournane1, J. Hardy3

1Département de Physique, Faculté des Sciences, Université Mouloud Mammeri de Tizi-Ouzou

B.P :17 RP, Tizi-Ouzou 15000, Algérie

2Laboratoire PEC, Université du Maine, 72085 Le Mans, France

1Laboratoire d’Acoustique, Université du Maine, 72085 Le Mans, France

* Corresponding author. E-mail: rachid.tigrine@univ-lemans.fr

Received : 08 March 2003 ; revised version accepted : 01 June 2003

Abstract

We present the solution of the full vibrational problem arising from the absence of translational symmetry in hexagonal two-dimensional crystals due to their different types of domain boundaries called heavy and superheavy solitons. In these cases, the defect is related to the parameter spacing and defect force constants. These perturbations in the homogeneity of the crystal give rises to localized vibration modes in its neighborhood. A detailed study is presented for the hexagonal two-dimensional crystal phonon localized states due to their different types of solitons. This study is conducted in the harmonic approximation with central nearest neighbor interactions. The localization properties are determined using the mathematical framework of the matching method which can be applied to analyze both the vibration and the scattering dynamic phenomena for soliton defects. We show the existence of optical and acoustical localized modes for heavy and superheavy solitons. The number and features of these curves depend strongly on the nature of the defect and system parameters.

Keywords: Two-dimensional crystals; Dynamical vibrations; Localized modes; Matching method.

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