Quasiparticle electronic structure and optical response ($G_0W_0$+BSE) of anatase TiO$_2$ starting from modified HSE06 functionals

TL;DR

This study combines a modified HSE06 functional with many-body perturbation theory to accurately predict the electronic and optical properties of anatase TiO$_2$, including exciton binding energies and transition characteristics.

Contribution

It introduces a modified HSE06(20) functional as an effective starting point for $G_0W_0$+BSE calculations on anatase TiO$_2$, improving agreement with experimental data.

Findings

Accurate prediction of quasiparticle band structure.

Exciton binding energy of 229 meV matching experiments.

Identification of excitonic states originating from specific band transitions.

Abstract

The quasiparticle electronic structure and optical excitation of anatase TiO$_2$ is determined within the framework of many-body perturbation theory (MBPT) by combining the $G_0W_0$ method and the Bethe-Salpeter Equation (BSE). A modified version of the HSE06 screened hybrid functional, that includes 20\% exact Fock exchange (HSE06(20)) as opposed to 25\% in the standard HSE06 functional, is used to set up the starting Hamiltonian for $G_0W_0$+BSE calculations. The HSE06(20) functional accurately predicts the ground state electronic band structure. BSE calculations based on data from $G_0W_0$+HSE06(20) yield direct optical excitation energies and oscillator strengths in excellent agreement with existing experiments and theoretical calculations characterizing direct excitation. In particular, an exciton binding energy of 229 $\pm$ 10 meV is obtained, in close agreement with experiments. The projections of excitonic states onto the quasiparticle band structure in a fatband representation shows that the lowest optical transition of anatase TiO$_2$ consists of excitons originating from the mixing of direct transitions within band pairs running parallel to the $\Gamma -Z $ direction in the tetragonal Brillouin zone. This implies a strong spatial localization of excitons in the $xy$ plane of the lattice. This investigation highlights the importance of a suitable non-interacting Hamiltonian for the MBPT based quasiparticle $G_0W_0$ and subsequent BSE calculations and suggests HSE06(20) as an optimal choice in the case of anatase TiO$_2$.