A Local Representation of the Electronic Dielectric Response Function

TL;DR

This paper introduces a fully ab initio local representation of the electronic dielectric response function, enabling the definition of local metrics like bond polarizability based on Wannier functions.

Contribution

It develops a novel local representation of the dielectric response function using Wannier functions and density functional perturbation theory, allowing for local analysis and modeling.

Findings

Dielectric response is exponentially localized in gapped systems.

Local response can be modeled with a tight-binding approach.

Allows rigorous definition of local dielectric metrics.

Abstract

We present a local representation of the electronic dielectric response function, based on a spatial partition of the dielectric response into contributions from each Wannier function using a generalized density functional perturbation theory. This procedure is fully ab initio, and therefore allows us to rigorously define local metrics, such as "bond polarizability," on Wannier centers. We show that the locality of the response function is determined by the locality of three quantities: Wannier functions of the occupied manifold, the density matrix, and the Hamiltonian matrix. In systems with a gap, the bare dielectric response is exponentially localized, which supports the physical picture of the dielectric response function as a collection of interacting local response that can be captured by a tight-binding model.