${\mathbb{Z}}_2$ Topological Invariant for Magnon Spin Hall Systems

Abstract

We propose a definition of a ${\mathbb{Z}}_2$ topological invariant for magnon spin Hall systems which are the bosonic analog of two-dimensional topological insulators in class AII. The existence of "Kramers pairs" in these systems is guaranteed by pseudo-time-reversal symmetry which is the same as time-reversal symmetry up to some unitary transformation. The ${\mathbb{Z}}_2$ index of each Kramers pair of bands is expressed in terms of the bosonic counterparts of the Berry connection and curvature. We construct explicit examples of magnon spin Hall systems and demonstrate that our ${\mathbb{Z}}_2$ index precisely characterizes the presence or absence of helical edge states. The proposed ${\mathbb{Z}}_2$ index and the formalism developed can be applied not only to magnonic systems but also to other non-interacting bosonic systems.

arXiv comment10 pages, 4 figures; v2: references added, typos corrected; v3: typos corrected. arXiv admin note: text overlap with arXiv:2006.10391

References in corpus (67)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Scheme to Achieve Silicon Topological Photonics
• Topological quantum chemistry
• Analogs of quantum Hall effect edge states in photonic crystals
• Hall Effect of Light
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Observation of the Magnon Hall Effect
• Topological classification of crystalline insulators through band structure combinatorics
• Theory of Thermal Hall Effect in Quantum Magnets
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Topological chiral magnonic edge mode in a magnonic crystal
• Hourglass Fermions
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Topological Nature of the Phonon Hall Effect
• On the $Z_2$ classification of Quantum Spin Hall Models
• Spin Nernst Effect of Magnons in Collinear Antiferromagnets
• The thermal Hall effect of spin excitations in a Kagome magnet
• Topological classification with additional symmetries from Clifford algebras
• Rotational motion of magnon and thermal Hall effect
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Quantum spin Hall effect in three dimensional materials: Lattice computation of Z${}_2$ topological invariants and its application to Bi and Sb
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Magnon spin Nernst effect in antiferromagnets
• A Realization of the Haldane-Kane-Mele Model in a System of Localized Spins
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Weyl magnons in breathing pyrochlore antiferromagnets
• Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators
• Scattering theory of topological insulators and superconductors
• Chiral spin-wave edge modes in dipolar magnetic thin films
• Berry Curvature and Phonon Hall Effect
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Topological non-symmorphic crystalline insulators
• Theory of Phonon Hall Effect in Paramagnetic Dielectrics
• Photon thermal Hall effect
• Tunable magnon Weyl points in ferromagnetic pyrochlores
• Hall effect of triplons in a dimerized quantum magnet
• Magnon Dirac materials
• K-Theory and Pseudospectra for Topological Insulators
• Magnonic topological insulators in antiferromagnets
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Spinless Topological Insulators without Time-Reversal Symmetry
• Signature of magnon Nernst effect in an antiferromagnetic insulator
• Equivalent topological invariants of topological insulators
• Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectric
• Magnonic Weyl semimetal in pyrochlore ferromagnets
• Thermal Hall effect in a phonon-glass Ba${}_3$CuSb${}_2$O${}_9$
• Origin of the Phonon Hall Effect in Rare-Earth Garnets
• Phonon Hall thermal conductivity from Green-Kubo formula
• Chirality-driven Hall Transport Phenomena of Spins
• Topological magnons in a kagome lattice spin system with $XXZ$ and Dzyaloshinskii-Moriya interactions
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• The $Z_2$ Index of Disordered Topological Insulators with Time Reversal Symmetry
• Magnonic Analogs of Topological Dirac Semimetals
• Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach
• Topological meaning of Z${}_2$ numbers in time reversal invariant systems
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder

Cited by in corpus (51)

• Symmetry and Topology in Non-Hermitian Physics
• Topological Magnons: A Review
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Topological insulators and semimetals in classical magnetic systems
• Interaction-stabilized topological magnon insulator in ferromagnets
• Thermal Hall effect, spin Nernst effect, and spin density induced by thermal gradient in collinear ferrimagnets from magnon-phonon interaction
• Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems
• Nonlinear magnon spin Nernst effect in antiferromagnets and strain-tunable pure spin current
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Topological Phases in Magnonics
• Symmetry and topological classification of Floquet non-Hermitian systems
• Three-dimensional topological magnon systems
• Topological magnetic excitations
• A Perspective on Magnon Spin Nernst Effect in Antiferromagnets
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Stacking-dependent topological magnons in bilayer CrI${}_3$
• Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach
• The Krein-Schrödinger Formalism of Bosonic BdG and Certain Classical Systems and Their Topological Classification
• ${\mathbb{Z}}_2$ topological quantum paramagnet on a honeycomb bilayer
• Magnon corner states in twisted bilayer honeycomb magnets
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Laser control of magnonic topological phases in antiferromagnets
• Magnonic Floquet Quantum Spin Hall Insulator in Bilayer Collinear Antiferromagnets
• Higher-order Topological Phases of Magnons in van der Waals Honeycomb Ferromagnets
• Topological Hybrids of Magnons and Magnon Bound Pairs
• Non-trivial topology of the quasi-one-dimensional triplons in the quantum antiferromagnet ${\text{BiCu}}_2{\text{PO}}_6$
• Topological Classification of Excitations in Quadratic Bosonic Systems
• Hinge Magnons from Non-collinear Magnetic Order in Honeycomb Antiferromagnet
• Dirac cones and mass terms in bosonic spectra
• A simple approach to characterizing band topology in bosonic pairing Hamiltonians
• Dirac Hamiltonians for bosonic spectra
• Discovering momentum-dependent magnon spin texture in insulating antiferromagnets: Role of the Kitaev interaction
• Squeezing-induced Topological Gap Opening on Bosonic Bogoliubov Excitations
• Fragility of ${\mathcal{Z}}_2$ topological invariant characterizing triplet excitations in a bilayer kagome magnet
• Zero-frequency chiral magnonic edge states protected by non-equilibrium topology
• Electric field induced thermal Hall effect of triplons in the quantum dimer magnets $X$CuCl${}_3$ ($X=$ Tl, K)
• Magnon Hall effect in antiferromagnetic lattices
• Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices
• Quantum geometry of bosonic Bogoliubov quasiparticles
• Higher-order Topological States in Chiral Split Magnons of Honeycomb Altermagnets
• Topological paramagnetic excitons of localized f electrons on the honeycomb lattice
• Determining the range of magnetic interactions from the relations between magnon eigenvalues at high-symmetry k points
• Topological Aspects of Antiferromagnets
• Magnon bands and transverse transport in a proposed two-dimensional $C{u}_2{F}_5$ ferrimagnet
• Pinch points and half moons encode Berry curvature
• Topological bosonic Bogoliubov excitations with sublattice symmetry
• Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices
• Predicted versatile topological nodal magnons in Tb-based icosahedral quasicrystal 1/1 approximants
• Topological phases of electrons induced by electron-magnon interactions
• Fate of Bosonic Topological Edge Modes in the Presence of Many-Body Interactions
• Topological Invariant for Bosonic Bogoliubov-de Gennes Systems with Disorder