Electron-electron interactions and lattice distortions in the perovskite titanates

A two-dimensional electron gas (2DEG) with the unprecedented high density of 3x10$^{14}$ (corresponding to 1/2 electron per interface unit cell area) can be formed at the interface between SrTiO$_3$ and a rare-earth titanate ($R$TiO$_3$). The 2DEG resides in the SrTiO$_3$, and arises from a polar discontinuity at the interface. The formation of this 2DEG has led us to study these perovskite titanates in detail. Some of these compounds are Mott insulators, where a Mott-Hubbard gap opens up between partially filled Ti 3$d$ bands. This talk focuses on the importance of the interplay between electron-electron interactions and lattice distortions in these complex oxides, which we study with density functional theory using a hybrid functional, capable of correctly describing electron localization and Mott-insulating behavior. These effects are crucial to understanding the metal-to-insulator transition as a function of electron density. Indeed, very thin SrTiO$_3$ layers inserted in GdTiO$_3$ show insulating behavior, in contrast to the metallic character of thicker layers in which the electrons form a 2DEG. The same physics is observed in bulk SrTiO$_3$ when doped with 1/2 electron per Ti atom \footnote{L. Bjaalie, A. Janotti, B. Himmetoglu, and C. G. Van de Walle, Phys. Rev. B. 90, 195117 (2014).}. Charge localization and lattice distortions also govern the formation of small hole polarons in the rare-earth titanates. We demonstrate that these polarons impact the optical absorption measurements commonly used to determine the value of the Mott-Hubbard gap \footnote{L. Bjaalie, D. G. Ouellette, P. Moetakef, T. A. Cain, A. Janotti, B. Himmetoglu, S. J. Allen, S. Stemmer and C. G. Van de Walle, Appl. Phys. Lett. 106, 232103 (2015).}. \\ \\ Work performed in collaboration with Anderson Janotti, Burak Himmetoglu, and Chris G. Van de Walle, and supported by NSF and ARO.