Design of Chern and Mott insulators in buckled3doxide honeycomb lattices

Abstract

Perovskite $(\mathrm{La}X{\mathrm{O}}_{3}){}_{2}/({\mathrm{LaAlO}}_{3}){}_{4}$(111) superlattices with $X$ spanning the entire $3d$ transition-metal series combine the strongly correlated, multiorbital nature of electrons in transition-metal oxides with a honeycomb lattice as a key feature. Based on density functional theory calculations including strong interaction effects, we establish trends in the evolution of electronic states as a function of several control parameters: band filling, interaction strength, spin-orbit coupling (SOC), and lattice instabilities. Competition between local pseudocubic and global trigonal symmetry as well as the additional flexibility provided by the magnetic and spin degrees of freedom of $3d$ ions lead to a broad array of distinctive broken-symmetry ground states not accessible for the (001)-growth direction, offering a platform to design two-dimensional electronic functionalities. Constraining the symmetry between the two triangular sublattices causes $X=\mathrm{Mn}$, Co, and Ti to emerge as Chern insulators driven by SOC. For $X=\mathrm{Mn}$ we illustrate how interaction strength and lattice distortions can tune these systems between a Dirac semimetal, a Chern and a trivial Mott insulator.