Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals

TL;DR

This paper demonstrates that Bloch symmetry can be maintained in orbital-density-dependent Koopmans-compliant functionals, allowing accurate band structure calculations in crystalline materials despite the localized nature of the variational orbitals.

Contribution

It introduces a method to preserve Bloch symmetry and unfold electronic bands in Koopmans-compliant functionals, enabling reliable band structure predictions.

Findings

Good agreement with experiments and many-body perturbation theory.

Method successfully applied to semiconductors and insulators.

Band structures can be accurately obtained from supercell calculations.

Abstract

Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the occupation of any orbital. In crystalline materials, due to the orbital-density-dependent nature of the functionals, minimization of the total energy to a ground state provides a set of minimizing variational orbitals that are localized and thus break the periodicity of the underlying lattice. Despite this, we show that Bloch symmetry can be preserved and it is possible to describe the electronic states with a band-structure picture, thanks to the Wannier-like character of the variational orbitals. We also present a method to unfold and interpolate the electronic bands from supercell ($\Gamma$-point) calculations, which enables us to calculate full band structures with Koopmans-compliant functionals. The results obtained for a set of benchmark semiconductors and insulators show very good agreement with state-of-the-art many-body perturbation theory and experiments, underscoring the reliability of these spectral functionals in predicting band structures.