# Optical properties of periodic systems within the current-current response framework: pitfalls and remedies

## TL;DR

This paper compares density-density and current-current response functions for optical absorption in extended systems, highlighting pitfalls and proposing remedies to ensure physical accuracy in calculations.

## Contribution

It identifies issues in current-based response calculations at zero momentum and offers corrected methods for including lifetime effects and electron-hole interactions.

## Key findings

- Incorrect velocity operator definitions cause unphysical spectra.
- Proper inclusion of lifetime effects improves spectral accuracy.
- Methodology applies to semiconductors, metals, and insulators.

## Abstract

We compare the optical absorption of extended systems using the density-density and current-current linear response functions calculated within many-body perturbation theory. The two approaches are formally equivalent for a finite momentum $\mathbf{q}$ of the external perturbation. At $\mathbf{q}=\mathbf{0}$, however, the equivalence is maintained only if a small $q$ expansion of the density-density response function is used. Moreover, in practical calculations this equivalence can be lost if one naively extends the strategies usually employed in the density-based approach to the current-based approach. Specifically we discuss the use of a smearing parameter or of the quasiparticle lifetimes to describe the finite width of the spectral peaks and the inclusion of electron-hole interaction. In those instances we show that the incorrect definition of the velocity operator and the violation of the conductivity sum rule introduce unphysical features in the optical absorption spectra of three paradigmatic systems: silicon (semiconductor), copper (metal) and lithium fluoride (insulator). We then demonstrate how to correctly introduce lifetime effects and electron-hole interactions within the current-based approach.