Critical analysis of the response function in low dimensional materials

TL;DR

This paper demonstrates that accurate prediction of charge or spin instabilities in low-dimensional materials requires calculating the full response function with matrix elements, challenging common simplified assumptions based on Fermi surface nesting.

Contribution

It shows through models and real materials that neglecting matrix elements leads to incorrect predictions of response function peaks and instabilities.

Findings

Constant matrix elements oversimplify the response function.

Including matrix elements alters or washes out predicted peaks.

Fermi surface nesting alone does not guarantee instabilities.

Abstract

The presence of sharp peaks in the real part of the static dielectric response function are usually accepted as indication of charge or spin instabilities in a material. However, there are misconceptions that Fermi surface (FS) nesting guarantees a peak in the response function like in one-dimensional systems, and, in addition, response function matrix elements between empty and occupied states are usually considered of secondary importance and typically set to unity like in the free electron gas case. In this work, we explicitly show, through model systems and real materials, within the framework of density functional theory, that predictions about the peaks in the response function, using FS nesting and constant matrix elements yields erroneous conclusions. We find that the inclusion of the matrix elements completely alters the structure of the response function. In all the cases studied other than the one-dimensional case we find that the inclusion of matrix elements washes out the structure found with constant matrix elements. Our conclusion is that it is imperative to calculate the full response function, with matrix elements, when making predictions about instabilities in novel materials.