3D Quantum Anomalous Hall Effect in Hyperhoneycomb Lattices

Abstract

We address the role of short range interactions for spinless fermions in the hyperhoneycomb lattice, a three dimensional (3D) structure where all sites have a planar trigonal connectivity. For weak interactions, the system is a line-node semimetal. In the presence of strong interactions, we show that the system can be unstable to a 3D quantum anomalous Hall phase with loop currents that break time reversal symmetry, as in the Haldane model. We find that the low energy excitations of this state are Weyl fermions connected by surface Fermi arcs. We show that the 3D anomalous Hall conductivity is $e^2/(\sqrt{3}ah)$, with $a$ the lattice constant.

5 pages, 5 figures

References in corpus (13)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Topological Mott Insulators
• Anomalous Hall Effect in Weyl Metals
• Potential ring of Dirac nodes in a new polymorph of Ca${}_3$P${}_2$
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Observation of topological transitions in interacting quantum circuits
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Theory of the Three Dimensional Quantum Hall Effect in Graphite
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Quantum Anomalous Hall Effect in Magnetic Insulator Heterostructure
• Stacking Faults, Bound States, and Quantum Hall Plateaus in Crystalline Graphite
• Universal phase transition and band structures for spinless nodal-line and Weyl semimetals

Cited by in corpus (10)

• Three-Dimensional Quantum Anomalous Hall Effect in Ferromagnetic Insulators
• Cubic 3D Chern photonic insulators with orientable large Chern vectors
• Microscopic polarization and magnetization fields in extended systems
• Spontaneous symmetry breaking of an interacting Chern insulator on a topological square lattice
• Hund nodal line semimetals: The case of twisted magnetic phase in the double-exchange model
• Elastic gauge fields and zero-field 3D quantum Hall effect in hyperhoneycomb lattices
• Three-dimensional quantum anomalous Hall effect in Weyl semimetals
• Emergence of asymmetric fermionic order in interacting birefringent fermions
• Quantum critical scaling of gapped phases in nodal-line semimetals
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response