Lattice distortion effects on topological phases in (LaNiO$_3$)$_2$/(LaAlO$_3$)$_N$ heterostructures grown along the [111] direction

TL;DR

This paper studies how internal and external strains affect topological phases in LaNiO3/LaAlO3 heterostructures grown along [111], revealing robustness of topological features against distortions and strain-induced gap openings.

Contribution

It provides a theoretical analysis combining Hartree-Fock and density functional theory to show strain effects on topological phases in [111]-oriented heterostructures, highlighting their robustness.

Findings

Quadratic band touching and Dirac points are stable under internal strain.

External strain can open a gap at the $b3$ point but not at Dirac points.

Strain influences magnetic and orbital order without destroying topological phases.

Abstract

We theoretically investigate the influence of internal and external strain on topological phases in (LaNiO$_3$)$_2$/(LaAlO$_3$)$_N$ heterostructures grown along the [111] direction. At the Hartree-Fock level, topological phases originate from an interaction-generated effective spin-orbit coupling that opens a gap in the band structure. For the unstrained system, there is a quadratic band touching at the $\Gamma$ point at the Fermi energy for unpolarized electrons and Dirac points at K, K$'$ at the Fermi energy for fully polarized electrons. Using density functional theory we show that the quadratic band touching and Dirac points are remarkably stable to internal strain-induced out-of-plane distortions and rotations of the oxygen octahedra, which we compute. The lack of a gap opening from internal strain implies a robustness to the mean-field predicted topological phases for both the polarized and unpolarized systems. We also consider an external strain imposed along the [001] cubic direction and show this can open a gap at the $\Gamma$ point but leaves the Dirac points intact. Finally, we compute a phase diagram for parameters relevant to LaNiO$_3$ which shows that strain favors a phase with polarized orbitals and antiferromagnetic spin order, but leaves earlier predictions for a zero-magnetic field topological quantum Hall state essentially unchanged. Taken together, our results suggest that the [111] growth direction in perovskites may lead to thin films that are relatively immune to distortion effects compared to those grown along [001].