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Analytical study of the edge states in the bosonic Haldane model
1Theoretical Physics Division, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.
Abstract:
We investigate the properties of magnon edge states in a ferromagnetic honeycomb spin lattice with a Dzialozinskii-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 the DMI strength. Our findings extend the predictions using topological arguments and they allow size-dependent confirmation from possible experiments.
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