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The difference between the edge on-site potential and the bulk values in amagnonic topological honeycomb lattice leads to the formation of edge states ina bearded boundary, and the same difference is found to be the responsible forthe absence of edge states in a zig-zag termination. In a finite lattice, theintrinsic on-site interactions along the boundary sites generate an effectivedefect and Tamm-like edge states appear for both zig-zag and beardedterminations. If a non-trivial gap is induced, Tamm-like and topologicallyprotected edge states appear in the band structure. The effective defect can bestrengthened by an external on-site potential and the dispersion relation,velocity and magnon-density of the edge states become tunable.

Edge on-site potential effects in a honeycomb topological magnon insulator