Eur. Phys. J. B 24, 297-304 (2001)
https://doi.org/10.1007/s10051-001-8677-2

Localized modes in a one-dimensional sphalerite-structure lattice with anharmonicity

¹ China Center of Advanced Science and Technology (World Laboratory), PO Box 8730, Beijing 100080, PR China
² Department of Physics and Institute of Nonlinear Physics, Hunan Normal University, Changsha 410081, PR China
³ International Center for Materials Physics, Chinese Academy of Sciences, Shnyang 110015, PR China
⁴ Department of Applied Physics, China Center South University, Changsha 410083, PR China

Corresponding author: ^a ghzhou@mail.hunnu.edu.cn

Received: 14 May 2001
Revised: 12 July 2001
Published online: 15 December 2001

Abstract

The nonlinear localized vibrational modes of a one-dimensional atomic chain with two periodically alternating masses and force constants are analytically investigated using a discrete multiple-scale expansion method. This model simulates a row of atoms in the 1 1 1-direction of sphalerite, or zinc blende, crystals. Owing to the structural asymmetry, the vibrational amplitude is governed by a perturbed nonlinear Schrödinger equation instead of the standard one found in one-dimensional lattices with two alternating masses but uniform force constant. Although the stationary localized modes with carrier wavevector at the Brillouin-zone boundary are similar to those of ionic lattices, the moving localized modes with wavevectors within the zone are different owing to the perturbation. The calculation shows that the height of the moving localized modes in this lattice dampens with time.