Dielectric properties of multiband electron systems: II - Collective modes

TL;DR

This paper investigates the collective electronic excitations in two-band systems using a tight-binding model within the random phase approximation, highlighting how symmetry and bandwidth influence modes and damping.

Contribution

It provides a detailed analysis of collective modes and electron-hole excitations in multiband systems, emphasizing the role of symmetry, bandwidth, and atomic transitions.

Findings

In insulators, only inter-band charge oscillations occur.

Atomic dipolar transitions lead to Frenkel excitons in the zero bandwidth limit.

Finite bandwidths affect mode dispersion and enable Landau damping.

Abstract

Starting from the tight-binding dielectric matrix in the random phase approximation we examine the collective modes and electron-hole excitations in a two-band electronic system. For long wavelengths (${\bf q}\rightarrow0$), for which most of the analysis is carried out, the properties of the collective modes are closely related to the symmetry of the atomic orbitals involved in the tight-binding states. In insulators there are only inter-band charge oscillations. If atomic dipolar transitions are allowed, the corresponding collective modes reduce in the asymptotic limit of vanishing bandwidths to Frenkel excitons for an atomic insulator with weak on-site interactions. The finite bandwidths renormalize the dispersion of these modes and introduce a continuum of incoherent inter-band electron-hole excitations. The possible Landau damping of collective modes due to the presence of this continuum is discussed in detail.