# Confinement-driven electronic and topological phases in corundum-derived $3d$-oxide honeycomb lattices

## TL;DR

This study uses density functional theory to explore electronic and topological phases in corundum-structured $3d$ transition metal oxide honeycomb layers, revealing tunable Dirac points, significant anomalous Hall effects, and potential realization of the topological Haldane model.

## Contribution

It demonstrates the emergence of topologically nontrivial phases and the influence of strain and spin-orbit coupling in corundum-derived $3d$-oxide honeycomb lattices, a novel structural context.

## Key findings

- Dirac points can be tuned to the Fermi level with strain.
- Spin-orbit coupling induces large anomalous Hall conductivity.
- Identification of a candidate system for the topological Haldane model.

## Abstract

Using density functional theory calculations including an on-site Coulomb term, we explore electronic and possibly topologically nontrivial phases in $3d$ transition metal oxide honeycomb layers confined in the corundum structure ($\alpha$-Al$_2$O$_3$) along the [0001] direction. In most cases the ground state is a trivial antiferromagnetic Mott insulator, often with distinct orbital or spin states compared to the bulk phases. With imposed symmetry of the two sublattices the ferromagnetic phases of Ti, Mn, Co and Ni exhibit a characteristic set of four bands, two relatively flat and two with a Dirac crossing at K, associated with the single electron occupation of $e_{g}'$ (Ti) or $e_{g}$ (Mn, Co, Ni) orbitals. Our results indicate that the Dirac point can be tuned to the Fermi level using strain. Applying spin-orbit coupling (SOC) leads to a substantial anomalous Hall conductivity with values up to 0.94 $e^2/h$. Moreover, at $a_{Al_2O_3}$=4.81\AA\ we identify a particularly strong effect of SOC with out-of-plane easy axis for ($Ti_2$O$_3$)$_1$/(Al$_2$O$_3$)$_5$(0001) which stabilizes dynamically the system. Due to the unusually high orbital moment of -0.88$\mu_{\rm B}$ that nearly compensates the spin moment of 1.01$\mu_{\rm B}$, this system emerges as a candidate for the realization of the topological Haldane model of spinless fermions. Parallels to the perovskite analogs (La$X$O$_3$)$_2$/(LaAlO$_3$)$_4$(111) are discussed.