Analytical study of the edge states in the bosonic Haldane model

Abstract

We investigate the properties of magnon edge states in a ferromagnetic honeycomb spin lattice with a Dzyaloshinskii-Moriya interaction (DMI). We derive analytical expressions for the energy spectra and wavefunctions of the edge states localized on the boundaries. By introducing an external on-site potential at the outermost sites, we show that the bosonic band structure is similar to that of the fermionic graphene. We investigate the region in the momentum space where the bosonic edge states are well defined and we analyze the width of the edge state and their dependence with DMI strength. Our findings extend the predictions using topological arguments and they allow size-dependent confirmation from possible experiments

7 pages, 4 figures (Minor corrections added)

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Cited by in corpus (13)

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• Photoinduced Topological Phase Transitions in Topological Magnon Insulators
• Edge states in a ferromagnetic honeycomb lattice with armchair boundaries
• Edge on-site potential effects in a honeycomb topological magnon insulator
• Unconventional Thermal Magnon Hall Effect in a Ferromagnetic Topological Insulator
• Photo-induced Entanglement in a Magnonic Floquet Topological Insulator
• Bulk-edge correspondence in two-dimensional topological semimetals: A transfer matrix study of antichiral edge modes
• Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models
• Explicit derivation of the chiral and (generic) helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation
• Nonlinear localized excitations in a topological ferromagnetic honeycomb lattice
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Electronic Manipulation of Magnon Topology by Chirality Injection from Boundaries
• Long-distance coupling of spin qubits via topological magnons