Coupling between ferroelectric distortions and excitonic properties in PbTiO$_3$

TL;DR

This paper addresses the challenge of accurately describing PbTiO3’s optical absorption and excitonic response under ferroelectric distortion. It combines G0W0 quasiparticle corrections with the Bethe-Salpeter equation in a model-BSE framework to track the continuous evolution from cubic to tetragonal PTO along a distortion pathway, using seven intermediate structures for convergence. The key finding is that the first absorption peak, initially triply degenerate in the cubic phase, splits into two anisotropic excitonic features (p1 and p2) as distortion grows, driven by Ti t2g level splitting and distinct orbital-transition channels (in-plane O-2p to Ti-dxy vs out-of-plane O-2p to Ti-dxz/dyz). This demonstrates a microscopic mechanism to tailor PTO’s optical properties with external electric fields, offering a route to tunable optoelectronic devices based on ferroelectric polarization control.

Abstract

PbTiO$_3$ is a ferroelectric perovskite semiconductor with favourable electronic and optical properties, making it suitable for a wide range of applications, including photo-catalysis and (opto)electronic devices. Despite its relevance, an accurate ab-initio description of the optical absorption spectrum and of the impact of ferroelectric distortion on the excitonic properties is still lacking. We combine $G_0W_0$ and Bethe-Salpeter Equation calculations to investigate the electronic and optical properties of PbTiO$_3$, tracking the evolution of its excitonic spectrum along the transition from the cubic paraelectric to the tetragonal ferroelectric phase. As the polar distortion increases, the first absorption peak of the cubic phase splits into two distinct features due to symmetry breaking, which partially lifts the degeneracy of the underlying excitonic state. Crucially, the distortion further introduces an in-plane/out-of-plane anisotropy in the spectra and controls the energy separation between the resulting excitonic branches. These findings highlight the potential for tuning the optical absorption properties of PbTiO$_3$ via the application of an external electric field.

Figures (7)

• Figure 1: a), b) panels: band structures of the cubic and tetragonal phases of PTO projected on the orbitals of interest. The Fermi energy $E_F$ is set to zero, while the arrows indicate the optical transitions and are coloured coded according to the spectral features they contribute to. c), d) panels: Corresponding mBSE optical absorption spectra. For the tetragonal phase, the $xx/yy$ and $zz$ components of the dielectric tensor are reported separately, along with the isotropic spectrum, calculated as an average among the components. The dashed vertical lines are located at the energies of the analysed peaks. Insets: Crystalline structure of the two phases of PTO. Pb ions in black, O in red, Ti in light blue.
• Figure 2: Isotropic optical absorption spectra for the paraelectric and ferroelectric structures obtained in the model-BSE and IPA (Independent Particle) approximations, together with the transition strengths of the main excitons. The excitons contributing to the peaks of interest are indicated by vertical (orange) lines and labelled ($e$).
• Figure 3: Isotropic optical absorption spectra for intermediate structures along the distortion from the paraelectric to the ferroelectric phase, obtained within the mBSE approximation. The marked peak positions highlight how the cubic $p_0$ feature progressively splits into the $p_1$ and $p_2$ branches as the polar distortion increases.
• Figure 4: Fatband plots of the excitons from \ref{['fig:ipa-mbse']}: exciton $e_0$ from the paraelectric structure splits into three excitons with different characters in the ferroelectric phase. The black dots outline the band structure, while the coloured circles indicate the amplitude of the BSE eigenvector at each point. Different colours refer to different valence-conduction band pairs.
• Figure 5: Equivalent of \ref{['fig:main-fig']} for the 320% distorted structure.