Dynamic Effective Charge of a Finite Linear Chain

Abstract

A formalism for calculating the dynamic effective charge induced on the atoms of a homopolar crystal by the presence of a surface is presented in the framework of the tight-binding approximation. The method is applied to a one-dimensional chain of two-electron atoms for the purposes of illustration and identification of the critical model parameters. The wave function of the chain is constructed from a linear combination of $s$-like and $p$-like atomic orbitals. In the infinite chain, symmetry requires the dynamic effective charge of each atom to vanish. The presence of the free ends in the finite chain, however, induces dynamic effective charges on the atoms which decay in magnitude with increasing distance from the ends. It is found that the important model parameters are the energy band gap and the hopping integral between $s$ and $p$ states centered on adjacent sites. The dependence of the dynamic effective charge on these two parameters is presented.