High Chern numbers in a perovskite-derived dice lattice (La$X$O$_3$)$_3$/(LaAlO$_3$)$_3$(111) with $X=$ Ti, Mn and Co

TL;DR

This study uses density-functional theory to explore the electronic and topological properties of LaXO3/LaAlO3 superlattices with a dice lattice structure, revealing potential for high Chern number topological phases.

Contribution

It systematically investigates the topological phases in dice lattice superlattices with different transition metals, highlighting the emergence of high Chern numbers and their dependence on symmetry and spin-orbit coupling.

Findings

Ferromagnetic phase exhibits spin-polarized half-metallic state with Dirac crossings.

Symmetry lowering causes band rearrangement and metal-insulator transition.

Spin-orbit coupling induces large anomalous Hall conductivity up to ~-3e^2/h.

Abstract

The dice lattice, containing a stack of three triangular lattices, has been proposed to exhibit nontrivial flat bands with nonzero Chern numbers, but unlike the honeycomb lattice it is much less studied. By employing density-functional theory (DFT) calculations with an on-site Coulomb repulsion term, we explore systematically the electronic and topological properties of (La$X$O$_3$)$_3$/(LaAlO$_3$)$_3$(111) superlattices with $X=$ Ti, Mn and Co, where a LaAlO$_3$ trilayer spacer confines the La$X$O$_3$ (L$X$O) dice lattice. In the absence of spin-orbit coupling (SOC) with symmetry constrained to P3, the ferromagnetic (FM) phase of the L$X$O(111) trilayers exhibits a distinct spin-polarized half-metallic state with multiple Dirac crossings and coupled electron-hole pockets around the Fermi energy. Symmetry lowering induces a significant rearrangement of bands and triggers a metal-to-insulator transition. Inclusion of SOC leads to a substantial anomalous Hall conductivity (AHC) around the Fermi energy reaching values up to $\sim-3e^2/h$ for $X=$ Mn and Co in P3 symmetry and both in- and out-of-plane magnetization directions in the first case and along [001] in the latter. The dice lattice emerges as a promising playground to realise nontrivial topological phases with high Chern numbers.