From chiral d-wave to nodal line superconductivity in the harmonic honeycomb lattices

Abstract

Motivated by the recent realization of the three-dimensional hyperhoneycomb and stripyhoneycomb lattices in lithium iridate (Li${}_2$IrO${}_3$), we study the possible spin-singlet superconducting states on the whole series of harmonic honeycomb lattices. Beginning with an isolated out-of-plane twist making the honeycomb lattice three-dimensional, we find that the chiral d$\pm$id state, well-known from the honeycomb lattice, is realized in the largest members of the series at low to intermediate doping. Along the twist, four chiral edge states form a two-dimensional dispersive band. Reducing the distance between the twists to form the smaller members of the harmonic honeycomb lattices, the degeneracy between the d-wave states is lifted, which finally destroys the chiral state. By analyzing the hyper- and stripyhoneycomb lattices and generalizing using the $D_{2h}$ point group of all the harmonic honeycomb lattices, we show that the superconducting state often belongs to the trivial irreducible representation. This state has nodal lines at low to intermediate doping, which is possible because the full lattice symmetry allows sign changes between different sets of bonds. We also find time-reversal symmetry broken states, which are either fully gapped or feature nodal points, in certain parts of the phase diagram. Finally, we draw a comparison between the states classified in terms of the $D_{2h}$ symmetries and those observed on the $D_{6h}$ honeycomb lattice.

References in corpus (36)

• Electric Field Effect in Atomically Thin Carbon Films
• Anyons in an exactly solved model and beyond
• Classification of topological insulators and superconductors in three spatial dimensions
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Chiral superconductivity from repulsive interactions in doped graphene
• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• The spin quantum Hall effect in unconventional superconductors
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Competing many-body instabilities and unconventional superconductivity in graphene
• Density waves and Cooper pairing on the honeycomb lattice
• A new spin-anisotropic harmonic honeycomb iridate
• Resonating valence bonds and mean-field d-wave superconductivity in graphite
• Functional renormalization group and variational Monte Carlo studies of the electronic instabilities in graphene near 1/4 doping
• Chiral d-wave superconductivity in doped graphene
• Exactly solvable Kitaev model in three dimensions
• Topological Classification and Stability of Fermi Surfaces
• On edge states in superconductor with time inversion symmetry breaking
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Possibility of High Tc Superconductivity in doped Graphene
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Heisenberg-Kitaev model on hyperhoneycomb lattice
• Weyl spin liquids
• Edge properties of the chiral d-wave superconducting state in doped graphene
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Unified theory of spiral magnetism in the harmonic-honeycomb iridates α, β, γ Li2IrO3
• Global phase diagram of a doped Kitaev-Heisenberg model
• Competition between d-wave and topological p-wave superconductivity in the doped Kitaev-Heisenberg model
• Loop-nodal and Point-nodal Semimetals in Three-dimensional Honeycomb Lattices
• Predominance of the Kitaev interaction in a three-dimensional honeycomb iridate: from ab-initio to spin model
• Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model
• Defects in the (d+id)-wave superconducting state in heavily doped graphene

Cited by in corpus (4)

• Domain walls in a chiral d-wave superconductor on the honeycomb lattice
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
• Robust semi-Dirac points and unconventional topological phase transitions in doped superconducting Sr2IrO4 tunnel coupled to t2g electron systems
• Barrier tunneling of the Loop-Nodal Semimetal in the Hyperhoneycomb lattice