Emergent chiral symmetry in non-bipartite kagome and pyrochlore lattices with spin-orbit coupling

Abstract

Chiral symmetry in energy bands appears as perfectly symmetric anti-bonding and bonding pairs of energy levels. It has only been observed in a few classes of models with a bipartite lattice structure or Bogoliubov-de-Gennes systems having the pairwise basis. We show that the non-bipartite kagome and pyrochlore lattices can host chiral symmetric bands when the strong spin-orbit coupling is introduced. There, the electrons hop to their neighbors by always converting the spin orientation up-side-down, which allows the up and down spin bases to form fictitious bipartite connections. The gauge invariant Wilson loop operator defined on a triangular unit serves as a marker to detect the presence of chiral symmetry, and using this property, the chiral operator is constructed. This allows us to access their topological symmetry classes that can easily change with small perturbations.

6 pages, 3 figures, 1 table, supplementary material

References in corpus (20)

• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Flat Bands in Slightly Twisted Bilayer Graphene
• Numerical studies of confined states in rotated bilayers of graphene
• Chiral Flat Bands: Existence, Engineering and Stability
• Quantum-Hall activation gaps in graphene
• Tetrahedral Magnetic Order and the Metal-Insulator Transition in the Pyrochlore Lattice of Cd2Os2O7
• Pyrochlore electrons under pressure, heat and field: shedding light on the iridates
• Spin--orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Zero-energy states in corrugated bilayer graphene
• Quantum anomalous Hall effect from inverted charge transfer gap
• Real space Berry curvature of itinerant electron systems with spin-orbit interaction
• Topological aspects of graphene: Dirac fermions and the bulk-edge correspondence in magnetic fields
• Regular-Triangle Trimer and Charge Order Preserving the Anderson Condition in the Pyrochlore Structure of CsW${}_2$O${}_6$
• Vacancy-Engineered Flat-Band Superconductivity in Holey Graphene
• Spin-orbit coupling and electronic charge effects in Mott insulators
• Coexistence of metallic and nonmetallic properties in the pyrochlore Lu${}_2$Rh${}_2$O${}_7$
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
• Pyrochlore Oxide Hg2Os2O7 on Verge of Metal-Insulator Boundary

Cited by in corpus (4)

• Pinch-point spectral singularity from the interference of topological loop states
• Energy symmetry and interlayer wave function ratio of tunneling electrons in partially overlapped graphene
• Effective spin model with anisotropic exchange interactions for the spin-orbit coupled Hubbard model at half-filling
• Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling