Comment on article "Line of Dirac Nodes in Hyperhoneycomb Lattices"

TL;DR

This paper critiques a recent claim that hyperhoneycomb lattices are 3D topological insulators, demonstrating through DFT and EHT calculations that the previous tight-binding model was inadequate and the conclusions invalid.

Contribution

The authors provide a critical analysis showing that the tight-binding model used in prior work does not accurately describe hyperhoneycomb lattices, invalidating earlier claims.

Findings

DFT and EHT calculations contradict the tight-binding model.

The tight-binding model is inadequate for hyperhoneycomb lattices.

Previous conclusions about topological insulator behavior are invalid.

Abstract

Recently, carbon hyperhoneycomb ($\mathcal{H}$-n) lattices have been proposed to be, through a one-$p$ orbital tight-binding (TB) model with nearest-neighbor (n.n.) hopping, a family of strong 3D topological insulators (K. Mullen, B. Uchoa and D. T. Glatzhofer, Phys. Rev. Lett. 115, 026403 (2015)) . In this Comment we show, through Density Functional Theory (DFT) and Extended H\"uckel Theory (EHT) calculations for the $\mathcal{H}$-0 lattice, that the TB Hamiltonian used by the authors is inadequate, invalidating the presented conclusions.