Anisotropic electronic structure and transport properties of the $\mathcal{H}$-$0$ hyperhoneycomb lattice

TL;DR

This study investigates the anisotropic electronic and transport properties of the $ ext{H}$-0 hyperhoneycomb carbon lattice, revealing orientation-dependent conductivity and emphasizing the importance of second-nearest neighbor interactions in understanding its electronic structure.

Contribution

The paper provides detailed electronic structure and transport calculations for the $ ext{H}$-0 hyperhoneycomb lattice, highlighting the significance of second-nearest neighbor interactions and correcting previous assumptions.

Findings

$ ext{H}$-0 exhibits strongly anisotropic electronic properties.

Transport behavior depends on crystalline orientation, being insulating or conducting.

Second-nearest neighbor interactions are crucial for accurate electronic structure modeling.

Abstract

Carbon, being one of the most versatile elements of the periodic table, forms solids and molecules with often unusual properties. Recently, a novel family of three-dimensional graphitic carbon structures, the so-called hyperhoneycomb lattices, has been proposed, with the possibility of being topological insulators [K. Mullen, B. Uchoa and D. T. Glatzhofer, Phys. Rev. Lett. 115, 026403 (2015)]. In this work, we present electronic structure calculations for one member ($\mathcal{H}$-0) of this family, using Density Functional Theory and non-equilibrium Green's functions transport calculations to show that the $\mathcal{H}$-0 structure should have strongly anisotropic electronic properties, being an insulator or a conductor depending on the crystalline orientation chosen for transport. Calculations in the framework of Extended H\"uckel Theory indicate that these properties can only be understood if one considers at least $2^{nd}$ nearest-neighbor interactions between carbon atoms, invalidating some of the conclusions of Ref. [K. Mullen, B. Uchoa and D. T. Glatzhofer, Phys. Rev. Lett. 115, 026403 (2015)], at least for this particular material.