Tuning two-dimensional electron (hole) gases at LaInO$_{3}$/BaSnO$_{3}$ interfaces: Impact of polar distortions, termination, and thickness

Two-dimensional election gases (2DEG), arising due to quantum confinement at interfaces between transparent conducting oxides, have received tremendous attention in view of electronic applications. The challenge is to find a material system that exhibits both a high charge-carrier density and mobility, at and even above room temperature. Here, we explore the potential of interfaces formed by two lattice-matched wide-gap oxides of emerging interest, $\textit{i.e.}$, the polar, orthorhombic perovskite LaInO$_{3}$ and the non-polar, cubic perovskite BaSnO$_{3}$, employing density-functional theory and many-body theory. We demonstrate that this material combination exhibits all the key features for reaching the goal. For periodic heterostructures, we find that the polar discontinuity at the interface is mainly compensated by electronic relaxation through charge transfer from the LaInO$_{3}$ to the BaSnO$_{3}$ side. This leads to the formation of a 2DEG hosted by the highly-dispersive Sn-$s$-derived conduction band and a 2D hole gas of O-$p$ character, strongly localized inside LaInO$_{3}$. Remarkably, structural distortions through octahedra tilts induce a depolarization field counteracting the polar discontinuity, and thus increasing the $critical$ (minimal) LaInO$_{3}$ thickness, $t_c$, required for the formation of a 2DEG. These polar distortions decrease with increasing LaInO$_{3}$ thickness, enhancing the polar discontinuity and leading to a 2DEG density of 0.5 electron per unit-cell surface. Interestingly, in non-periodic heterostructures, these distortions lead to a decrease of $t_c$, thereby enhancing and delocalizing the 2DEG. We rationalize how polar distortions, termination, and thickness can be exploited in view of tailoring the 2DEG characteristics, and why this material is superior to the most studied prototype LaAlO$_{3}$/SrTiO$_{3}$.