Dielectric properties of multiband electron systems: I - Tight-binding formulation

TL;DR

This paper develops a tight-binding formulation for the dielectric properties of multiband electron systems, accounting for various polarization processes and analyzing the effects of atomic orbital symmetry on inter-band and intra-band interactions.

Contribution

It introduces a comprehensive dielectric matrix in the tight-binding framework that includes site-site, site-bond, and bond-bond correlations, with analysis of their significance.

Findings

Bond contributions are negligible at long wavelengths.

Dielectric matrix simplifies to 2x2 for two non-overlapping bands.

Inter-band and intra-band polarizations are separated in systems without dipolar transitions.

Abstract

The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site correlations, also the site-bond and bond-bond correlations, and thus includes all physically relevant polarization processes. The arguments are given that the bond contributions are negligible in the long wavelength limit. We analyse the system with two non-overlapping bands in this limit, and show that the corresponding dielectric matrix reduces to a $2\times2$ form. The intra-band and inter-band contributions are represented by diagonal matrix elements, while the off-diagonal elements contain the mixing between them. The latter is absent in insulators but may be finite in conductors. Performing the multipole expansion of the bare long-range interaction, we show that this mixing is directly related to the symmetry of the atomic orbitals participating in the tight-binding electronic states. In systems with forbidden atomic dipolar transitions, the intra-band and inter-band polarizations are separated. However, when the dipolar transitions are allowed, the off-diagonal elements of the dielectric matrix are of the same order as diagonal ones, due to a finite monopole-dipole interaction between the intra-band and inter-band charge fluctuations.