Real-space approach to calculation of electric polarization and dielectric constants

TL;DR

This paper introduces a real-space iterative method using Wannier functions to compute electric polarization and dielectric constants of insulators under applied electric fields, demonstrated on a 1D model.

Contribution

It presents a novel real-space approach leveraging Wannier functions for calculating polarization and dielectric properties in non-zero electric fields.

Findings

Method successfully applied to a 1D tight-binding model.

Accurately computes polarization and dielectric constants under electric fields.

Provides a new computational tool for insulating materials analysis.

Abstract

We describe a real-space approach to the calculation of the properties of an insulating crystal in an applied electric field, based on the iterative determination of the Wannier functions (WF's) of the occupied bands. It has been recently shown that a knowledge of the occupied WF's allows the calculation of the spontaneous (zero-field) electronic polarization. Building on these ideas, we describe a method for calculating the electronic polarization and dielectric constants of a material in non-zero field. The method is demonstrated for a one-dimensional tight-binding Hamiltonian.