Topological and magnetic phases with strong spin-orbit coupling on the hyperhoneycomb lattice

Abstract

We study the general phase diagram of correlated electrons for iridium-based (Ir) compounds on the hyperhoneycomb lattice---a crystal structure where the Ir${}^{4+}$ ions form a three-dimensional network with three-fold coordination recently realized in the $\beta$-Li${}_2$IrO${}_3$ compound. Using a combination of microscopic derivations, symmetry analysis, and density functional calculations, we determine the general model for the electrons occupying the $j_{\text{eff}}=1/2$ orbitals at the Ir${}^{4+}$ sites. In the non-interacting limit, we find that this model allows for both topological and trivial electronic band insulators along with metallic states. The effect of Hubbard-type electron-electron repulsion on the above electronic structure in stabilizing $\mathbf{q}=0$ magnetic order reveals a phase diagram with continuous phase transition between a topological band insulator and a Neel ordered magnetic insulator.

11 pages, 7 figures

References in corpus (10)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Correlated quantum phenomena in the strong spin-orbit regime
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Antiferromagnetic topological insulators
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Crystal field splitting and correlation effect on the electronic structure of A2IrO3
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Order-by-disorder and magnetic field response in Heisenberg-Kitaev model on a hyperhoneycomb lattice

Cited by in corpus (13)

• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• Symmetry Demanded Topological Nodal-line Materials
• The Challenge of Spin-Orbit-Tuned Ground States in Iridates
• Long-range Coulomb interaction in nodal-ring semimetals
• Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Loop-nodal and Point-nodal Semimetals in Three-dimensional Honeycomb Lattices
• Order-by-disorder and spin-orbital liquids in a distorted Heisenberg-Kitaev model
• Two iridates, two models, two approaches: a comparative study on magnetism in 3D honeycomb materials
• Weyl and nodal ring magnons in three-dimensional honeycomb lattices
• Emergent quantum phases in a frustrated J1-J2 Heisenberg model on hyperhoneycomb lattice
• Lattice dynamics and structural transition of the hyperhoneycomb iridate $\beta$-Li${}_2$IrO${}_3$ investigated by high-pressure Raman scattering
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice