The interaction of intrinsic localized modes in the gap of doped semiconductors with plasmons

We present a theoretical investigation of the interaction of intrinsic localized modes with plasmons. The anharmonic localized modes for a ID diatomic lattice are determined using a two-body potential which describes the interactions among particles in a zinc-blende structure material. The localized mode frequency is inside the gap between acoustic and optical phonons. Calculations have been performed for GaN because it has a large phonon gap, can be highly n-doped, and the plasma frequency of free carriers is in the range of phonon and intrinsic localized mode frequencies. To study the coupling we add to the equations of motion an electric field to simulate the plasmon. Solving the system we obtain the dynamical displacements pattern from which we evaluate the total polarization. From the polarization we determine the frequency of the combined mode for which the dielectric function is zero. In this investigation we have analysed both the case of small localized mode amplitudes and the case of larger amplitudes, obtaining different behaviour. In the first case the mixed mode has a frequency above the top of the optical branch, which can be explained in terms of the theory of the harmonic dielectric response of polar lattice vibrations. In the second case the coupled mode exists only for a finite slab, and its frequency is inside the phonon gap.