Quasiparticle and optical band gaps of Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ from \textit{ab-initio} many-body perturbation theory

The Ruddlesden Popper homologous series Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$ provides a unique opportunity to study the effect of dimensionality and confinement on the band gap and absorption spectrum of the complex oxide SrTiO$_3$. In this work, we use many-body perturbation theory within the \textit{GW} approximation and the Bethe-Salpeter equation (BSE) approach to study the electronic and optical properties of Sr$_{n+1}$Ti$_{n}$O$_{3n+1}$. We find that our \textit{GW}/BSE direct and indirect band gaps are in excellent agreement with measured direct and indirect optical gaps. We discuss technical aspects of the calculations such as convergence and starting-point dependence, and compare to higher levels of theory. In addition, we find a relatively large exciton binding energy of 500 meV for Sr$_2$TiO$_4$ ($n=1$). We explore the role of structural distortions and epitaxial strain in the properties of the localized exciton. Our work suggests that layered structures can provide a viable route for the design of complex oxide materials with desirable optoelectronic properties. This work is supported by DOE.