THE TIGHT-BINDING APPROACH TO THE DIELECTRIC RESPONSE IN THE MULTIBAND SYSTEMS

TL;DR

This paper develops a tight-binding approach within the random phase approximation to analyze the dielectric response of multiband electron systems, highlighting collective modes, dielectric instabilities, and self-polarization effects.

Contribution

It introduces a tight-binding framework for dielectric response in multiband systems, emphasizing multipole expansion and collective mode analysis, with insights into dielectric instabilities and self-polarization corrections.

Findings

Identification of collective modes in cubic lattices.

Demonstration of dielectric instability via mode softening.

Clarification of self-polarization effects in finite band systems.

Abstract

Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with respect to the usual plane-wave decomposition are pointed out. The analysis becomes particularly transparent in the long wavelength limit, after performing the multipole expansion of bare Coulomb matrix elements. For illustration, the collective modes and the macroscopic dielectric function for a general cubic lattice are derived. It is shown that the dielectric instability in conducting narrow band systems proceeds by a common softening of one transverse and one longitudinal mode. Furthermore, the self-polarization corrections which appear in the macroscopic dielectric function for finite band systems, are identified as a combined effect of intra-atomic exchange interactions between electrons sitting in different orbitals and a finite inter-atomic tunneling.