Design of Chern and Mott insulators in buckled $3d$ oxide honeycomb lattices

Perovskite $\left(\mathrm{La}X{\mathrm{O}}_3\right){}_2/\left({\mathrm{LaAlO}}_3\right){}_4$(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.

Figure 1

Electronic ground [(a), (b), (d)] and selected metastable states [(c), (e)–(g)] in $(\mathrm{La}X{\mathrm{O}}_3{)}_2/{\left({\mathrm{LaAlO}}_3\right)}_4$(111) for $t_{2g}$ systems $X=\mathrm{Ti}$, V, Cr. The majority (minority) bands are shown in blue (orange), for the isosurfaces of the spin density majority (minority) are in blue (red). In cases (a), (e)–(g), the integration range is from $E_{\mathrm{F}}$-1 eV to $E_{\mathrm{F}}$ to emphasize the orbital polarization. Energies of metastable states are provided in red.

Figure 2

Same as Fig. 1, but for $e_g$ systems $X=\mathrm{Mn}$, Fe, Co, Ni, and Cu. A common feature is a set of four bands: two nearly flat and two crossing at K and ${\mathrm{K}}^{\prime }$. Despite the formally different band filling in $X=\mathrm{Mn}$, Co, Ni the Dirac points are pinned at the Fermi level within P321 symmetry (a)–(c), while symmetry breaking results in a gap opening (d)–(g). Further metastable phases are shown in (i)–(l).

Figure 3

Effect of SOC on $\left(\mathrm{La}X{\mathrm{O}}_3\right){}_2/\left({\mathrm{LaAlO}}_3\right){}_4$ (111) within P321 symmetry: (a) band inversion and gap opening for $X=\mathrm{Ti}$ with out-of-plane magnetization; (c) for $X=\mathrm{Mn}$ SOC with magnetization along [100] opens a substantial gap of 0.2 eV and lifts the degeneracy at $\mathrm{\Gamma }$; (b) and (d) calculated AHC versus (rigid band) chemical potential in units of $\left(e^2/h\right)$ indicates quantization of AHC in both cases. Small deviations from the integer value for $X=\mathrm{Ti}$ are likely due to other trivial pockets around the Fermi level.

Figure 4

Transition between the Chern insulating phase within P321 symmetry and the Mott insulating ground state in $\left(\mathrm{La}X{\mathrm{O}}_3\right){}_2/\left({\mathrm{LaAlO}}_3\right){}_4$(111). The band structures (a)–(c) show that a crossover of the gap sizes at K and M occurs already for the first geometry along the path (GEO1) which is metallic with a crossing along K-M. (d) evolution of band gap at K and M as a function of JT distortion expressed in the maximum deviation of the Mn-O distance from the average distance in the ${\mathrm{MnO}}_6$ octahedron. The shaded area denotes the supposed metallic region.

Figure 5

Influence of SOC with magnetization axis along [001] on the band structure of $\left({\mathrm{LaCoO}}_3\right){}_2\left({\mathrm{LaAlO}}_3\right){}_4$(111) within P321 symmetry. Note the gap opening at K and the lifting of degeneracy at $\mathrm{\Gamma }$.

Figure 6

Band structure (top row) and corresponding anomalous Hall conductivity in units of quantum conductance $\left(e^2/h\right)$ (bottom row) of $\left({\mathrm{LaMnO}}_3\right){}_2/\left({\mathrm{LaAlO}}_3\right){}_4$ as a function of Hubbard $U$ in P321 symmetry. Note that the band gap at K opens above $U=3$ eV, $J=0.7$ eV.