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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.
Compression dramatically changes the transport and localization properties of graphene. This is intimately related to the change of symmetry of the Dirac cone when the particle hopping is different along different directions of the lattice. In partic
Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals po
In an ordinary three-dimensional metal the Fermi surface forms a two-dimensional closed sheet separating the filled from the empty states. Topological semimetals, on the other hand, can exhibit protected one-dimensional Fermi lines or zero-dimensiona
We propose and characterize a new $mathbb{Z}_2$ class of topological semimetals with a vanishing spin--orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac Line Nodes (DLNs) and t
Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which exploits the Neel vector to control the topological electronic states and the associated spin-dependent transport properties. A recently discovered Neel spin-orbi