Sum Rules for the Coupled Plasmon-Optical-Phonon System

Abstract

In the presence of free carriers, longitudinal optical phonons in a polar semiconductor are coupled by electrostatic interaction to plasmon. These coupled modes of the plasmon and optical phonon system constitute longitudinal collective excitation in the semiconductor. As the concentration of carriers changes, the frequency of plasmon and consequently that of coupled modes change. The frequency shift of these collective modes should obey the following relations:
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where n is the number of ions in a unit cell; Ω_lμ Ω_tμ Ω_lμ⁽⁰⁾ are the angular frequency of longitudinal coupled modes, transverse optical phonon and that of longitudinal optical phonon in the absence of free carriers; ε₀ and ε_∞ are static and high frequency dielectric constant in the absence of free carriers; ω_p²=4πn₀e²⁄m^*ε_∞ which is the classical plasma frequency of the carrier.