Spectral properties of waves in superlattices with 2D and 3D inhomogeneities
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Spectral Properties of Waves in Superlattices with 2D and 3D Inhomogeneities V. A. Ignatchenko and D. S. Tsikalov L.V. Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia email: [email protected] Received May 11, 2010
Abstract—We investigate the dynamic susceptibility and onedimensional density of states in an initially sinusoidal superlattice containing simultaneously 2D phase inhomogeneities simulating correlated rough nesses of superlattice interfaces and 3D amplitude inhomogeneities of the superlattice layer materials. The analytic expression for the averaged Green’s function of the sinusoidal superlattice with two phase inho mogeneities is derived in the Bourret approximation. It is shown that the effect of increasing asymmetry in the peak heights of dynamic susceptibility at the Brillouin zone boundary of the superlattice, which was dis covered earlier [15] upon an increase in rootmeansquare (rms) fluctuations, also takes place upon an increase in the correlation wavenumber of inhomogeneities. However, the peaks in this case also become closer, and the width and depth of the gap in the density of states decrease thereby. It is shown that the enhancement of rms fluctuations of 3D amplitude inhomogeneities in a superlattice containing 2D phase inhomogeneities suppresses the effect of dynamic susceptibility asymmetry and leads to a slight broadening of the gap in the density of states and a decrease in its depth. Targeted experiments aimed at detecting the effects studied here would facilitate the development of radiospectroscopic and optical methods for identi fying the presence of inhomogeneities of various dimensions in multilayer magnetic and optical structures. DOI: 10.1134/S1063776111080061
1. INTRODUCTION In the last two decades, theoretical studies have been developed intensely on the effect of inhomoge neities in the geometrical structure of initially periodic superlattices on the spectral properties of waves of var ious nature or electronic excitations propagating in such media. For this purpose, computer simulation methods were mainly employed. In these studies, one dimensional (1D) geometrical disorder was consid ered as a rule, which was simulated either by violation of periodicity in the arrangement of the layers of vari ous materials forming superlattices or by random devi ations in the thickness of these layers. Various analyti cal approaches were also developed. The Green’s’s function method was used for investigating such struc tures in [1–3]. In the proposed model [4], the method of averaged Green’s functions was proposed for approximate analysis of geometrical 1D, 2D, and 3D disorder in superlattices with a sinusoidal profile of the dependence of a material parameter on the z coordi nate in the initial state (assuming that the z axis is per pendicular to the plane of the layers in the superlat tice). Inhomogeneities in such a superlattice were sim ulated by introducing a random phase u(x) into the harmo
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