Electronic Collective Modes for Systems with Two Effective Masses

Electronic collective modes (plasmons) are essential to the screening of Coulomb interactions and the optical properties of metals. In conventional 3D metals these collective modes, called plasmons, are optical in nature and can be probed with light. There are other, typically low-dimensional systems where the plasmon energy varies linearly or as a square root with its wavevector q. David Pines proposed that in a 3D material with two species of charge carriers, one light and one heavy, acoustic plasmons may form. We present the derivation of the dielectric function for N bands in D dimensions. We apply this result to calculate the plasmon spectrum for two species of charge carriers and discuss the result and its implication for the observation of acoustic plasmons in 3D materials.