Proper ab-initio dielectric function of 2D materials and their polarizable thickness

TL;DR

This paper introduces a formalism to accurately compute the dielectric function of 2D materials, accounting for intra- and inter-layer polarizability, enabling both single-layer analysis and stacking into heterostructures.

Contribution

It develops a formalism with profile functions to separate intra- and inter-layer contributions, facilitating ab-initio calculations and stacking of 2D materials.

Findings

Allows computation of single-layer dielectric functions from periodic calculations

Enables stacking of 2D layers to form heterostructures

Provides a method to determine effective thickness and polarizability

Abstract

In this paper we derive a formalism allowing us to separate inter-layer contributions to the polarizability of a periodic array of 2D materials from intra-layer ones. To this aim, effective profile functions are introduced. They constitute a tight-binding-like layer-localized basis involving two lengths, the effective thickness $d$ characteristic of the 2D material and the inter-layer separation $L$. The method permits, within the same formalism, either to compute the single-layer dielectric function from an ab-initio periodic calculation (top-down strategy) or to stack several 2D materials to generate a finite-thickness van der Waals heterostructure (bottom-up strategy).