Line of Dirac Nodes in Hyper-Honeycomb Lattices

TL;DR

This paper introduces 3D lattice models with Dirac loops, revealing unique electronic properties such as quantized Hall conductivities and topological surface states, with potential realization in carbon allotropes.

Contribution

It presents a new class of 3D lattice models with Dirac loops, extending the concept of Dirac points in graphene to three dimensions with novel topological features.

Findings

Presence of Dirac loops with linearly vanishing density of states

Quantized Hall conductivities in three dimensions for toroidal magnetic fields

Topological surface states in structures with spin-orbit coupling

Abstract

We propose a family of free fermion lattice models that have "Dirac loops", closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply-connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility of realizing the structures as new allotropes of carbon.