3D quantum Hall effects in Dirac loops

Nodal line semimetals describe a new class of 3D systems where the low energy bands have Dirac quasiparticles along a closed line in momentum space (Dirac loop) rather than a discrete set of Dirac points. Away from half filling, the Fermi surface is a toroid. In the presence of spin orbit coupling effects, those systems can behave as strong topological insulators, with topologically protected surface states.  In spite of being three dimensional, nodal line semimetals may have Landau level quantization at finite magnetic field for a certain field geometry. One conceptually interesting family of lattice models that realizes this physics is the family of the hyperhoneycomb lattices, which forms a 3D structure of crossed 1D chains where all sites have the same planar trigonal connectivity of graphene. In this talk, I will show that Coulomb interactions could drive the system to show an anomalous quantum Hall effect (AQHE), with current loops that produce zero net flux in the 3D unit cell. In the AQH state, I will show that the AQH gap has nodes along the Dirac loop, giving rise to pairs of Weyl points connected by Fermi arcs. I will discuss the anomalous Hall conductivity of this system, which carries charge through topologically protected surface states, and the Hall response of the system to strain field deformations of the lattice.