[Paper Review] A Theory for Colors of Strongly Correlated Electronic Systems

Swagata Acharya, Cédric Weber+4 more|arXiv (Cornell University)|Apr 23, 2022

Advanced Chemical Physics Studies4 citations

TL;DR

This paper develops an ab initio many-body theory to explain the optical colors of strongly correlated transition metal oxides and fluorides, such as green NiO and pink MnF2. By combining quasi-particle GW and Bethe-Salpeter equation (BSE) approaches with dynamical mean-field theory (DMFT), it identifies that spin-flip processes—absent in standard perturbative GW—determine the optical brightness of excitons in MnF2, while in NiO, triplet charge excitations with preserved spin configuration explain its green color.

ABSTRACT

Many strongly correlated transition metal insulators are colored, even though they have large fundamental band gaps and no quasi-particle excitations in the visible range. Why such insulators possess the colors they do poses a serious challenge for any many-body theory to reliably pick up the interactions responsible for the color. We pick two archetypal cases as examples: NiO with green color and MnF extsubscript{2} with pink color. The body of literature around the collective charge transitions (excitons) that are responsible for the color in these and other strongly correlated systems, often fail to disentangle two important factors: what makes them form and what makes them optically bright. An adequate answer requires a theoretical approach able to compute such excitations in periodic crystals, reliably and without free parameters -- a formidable challenge. We employ two kinds of advanced \emph{ab initio} many body Green's function theories to investigate both optical and spin susceptibilities. The first, a perturbative theory based on low-order extensions of the $GW$ approximation, is able to explain the color in NiO, and indeed well describe the dielectric response over the entire frequency spectrum, while the same theory is unable to explain why MnF extsubscript{2} is pink. We show its color originates from higher order spin-flip transitions that modify the optical response. This phenomenon is not captured by low-order perturbation theory, but it is contained in dynamical mean-field theory (DMFT), which has a dynamical spin-flip vertex that contributes to the charge susceptibility. We show that symmetry lowering mechanisms, such as spin-orbit coupling, odd-parity phonons and Jan-Teller distortions, determine how `bright' these excitons are, but are not fundamental to their existence.

Motivation & Objective

• To resolve why strongly correlated insulators like NiO and MnF2 exhibit visible color despite large band gaps and no low-energy quasiparticle excitations.
• To disentangle the physical origin of exciton formation from their optical brightness in correlated systems.
• To develop a parameter-free theoretical framework capable of computing dielectric response and optical susceptibilities in periodic crystals with strong electron correlations.
• To determine whether standard perturbative GW approaches suffice to explain optical properties or if higher-order correlations (e.g., spin-flip vertices) are essential.

Proposed method

• Employed quasi-particle self-consistent GW (QS GW) and QS $G\widehat{W}$ to compute accurate electronic band structures and self-energy corrections for NiO and MnF2.
• Used the Bethe-Salpeter equation (BSE) with vertex corrections to calculate excitonic states and dielectric response in the paramagnetic and antiferromagnetic phases.
• Applied dynamical mean-field theory (DMFT) to include non-perturbative spin-flip vertex contributions absent in standard GW, particularly relevant for MnF2.
• Performed simulations in both paramagnetic (quasi-random spin disorder) and antiferromagnetic (2×2×2 supercell) phases to compare optical responses.
• Used orbital, momentum, and real-space decomposition of excitons to analyze their spatial extent and character (e.g., d, p, O, Mn, Ni).
• Conducted convergence tests on BSE Hamiltonian size (up to 64 valence and conduction bands) to ensure reliable excitonic eigenvalues.

Experimental results

Research questions

• RQ1 Why do strongly correlated insulators like NiO and MnF2 exhibit visible color despite large fundamental band gaps and no quasiparticle excitations in the visible range?
• RQ2 What physical mechanism determines the optical brightness of collective charge excitations (excitons) in these materials?
• RQ3 Why does standard perturbative GW + BSE fail to explain the pink color of MnF2 but succeeds for NiO’s green color?
• RQ4 To what extent do symmetry-lowering effects (e.g., spin-orbit coupling, Jahn-Teller distortions) influence exciton brightness without affecting their existence?
• RQ5 Can DMFT capture the spin-flip vertex contributions necessary to explain the optical response in MnF2, which are missing in standard GW?

Key findings

• The green color of NiO arises from triplet charge excitations between t2g and eg orbitals that preserve the S=1 spin configuration, and this is well described by low-order GW + BSE.
• The pink color of MnF2 originates from higher-order spin-flip transitions that modify the electron-hole vertex and are not captured by perturbative GW, but are included in DMFT.
• In MnF2, the paramagnetic phase remains transparent within standard GW + BSE, but becomes colored only when the spin-flip component of the vertex is included via DMFT.
• Excitons in NiO (1.6 eV, Eb=2.4 eV) and CrI3 (1.1 eV, Eb=1.4 eV) are localized to ~4 Å, while in MoS2 (1.95 eV, Eb=0.55 eV) they extend over several nanometers.
• QS $G\widehat{W}$ reduces the QS GW band gap in NiO by ~1.0 eV, bringing it closer to experiment (4.0 eV vs. ~3.5–4.0 eV experimental), and improves d-p alignment.
• The BSE eigenvalue convergence is achieved with 64 valence and 64 conduction bands, indicating that a matrix size of 32,768 is sufficient for accurate excitonic spectra.