A way to identify whether a DFT gap is from right reasons or error cancellations: The case of copper chalcogenides

TL;DR

This paper investigates why common computational methods fail to predict the band gap in copper chalcogenides, revealing that correcting orbital splitting can accurately reproduce experimental gaps and distinguish genuine effects from error cancellations.

Contribution

It introduces a correction approach using hybrid pseudopotentials to accurately predict the band gap and provides a method to identify whether a computed gap is physically meaningful or due to error cancellation.

Findings

Correcting orbital splitting opens experimental magnitude gaps.

Standard methods underestimate the 4s-3d orbital splitting.

The approach distinguishes genuine electronic effects from error artifacts.

Abstract

Gap opening remains elusive in copper chalcogenides (Cu$_{2}X$, $X$ = S, Se and Te), not least because Hubbard + $U$, hybrid functional and ${GW}$ methods have also failed. In this work, we elucidate that their failure originates from a severe underestimation of the 4$s$-3$d$ orbital splitting of the Cu atom, which leads to a band-order inversion in the presence of an anionic crystal field. As a result, the Fermi energy is pinned due to symmetry, yielding an invariant zero gap. Utilizing the hybrid pseudopotentials to correct the underestimation on the atomic side opens up gaps of experimental magnitude in Cu$_{2}X$, suggesting their predominantly electronic nature. Our work not only clarifies the debate about the Cu$_{2}X$ gap, but also provides a way to identify which of the different methods really captures the physical essence and which is the result of error cancellation.