Loop-nodal and Point-nodal Semimetals in Three-dimensional Honeycomb Lattices

TL;DR

This paper introduces a broad class of three-dimensional honeycomb lattices that exhibit loop-nodal and point-nodal semimetal properties, with unique edge states and topological phases influenced by spin-orbit interaction.

Contribution

It proposes new 3D honeycomb lattice models as loop-nodal semimetals and explores their edge states, flat bands, and topological phases, including the effects of spin-orbit interaction.

Findings

Edge states have properties similar to 2D honeycomb lattices.

Partial flat bands appear at zigzag or beard edges.

All lattices become strong topological insulators with spin-orbit coupling.

Abstract

Honeycomb structure has a natural extension to the three dimensions. Simple examples are hyperhoneycomb and stripy-honeycomb lattices, which are realized in $\beta $-Li$_{2}$IrO$_{3}$ and $\gamma $-Li$_{2}$IrO$_{3}$, respectively. We propose a wide class of three-dimensional (3D) honeycomb lattices which are loop-nodal semimetals. Their edge states have intriguing properties similar to the two-dimensional honeycomb lattice in spite of dimensional difference. Partial flat bands emerge at the zigzag or beard edge of the 3D honeycomb lattice, whose boundary is given by the Fermi loop in the bulk spectrum. Analytic solutions are explicitly constructed for them. On the other hand, perfect flat bands emerge in the zigzag-beard edge or when the anisotropy is large. All these 3D honeycomb lattices become strong topological insulators with the inclusion of the spin-orbit interaction. Furthermore, point-nodal semimetals may be realized in the presence of both the antiferromagnetic order and the spin-orbit interaction.