Edge states at the boundary between topologically equivalent lattices

Abstract

Edge currents of paramagnetic colloidal particles propagate at the edge between two topologically equivalent magnetic lattices of different lattice constant when the system is driven with periodic modulation loops of an external magnetic field. The number of topologically protected particle edge transport modes is not determined by a bulk-boundary correspondence. Instead, we find a rich variety of edge transport modes that depend on the symmetry of both the edge and the modulation loop. The edge transport can be ratchet-like or adiabatic, and time or non-time reversal symmetric.

arXiv comment16 pages, 7 figures

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• Complete absorption of topologically protected waves
• Disorder scattering in classical flat channel transport of particles between twisted magnetic square patterns
• Topologically cloaked magnetic colloidal transport
• Topological sorting of magnetic colloidal bipeds
• Magnetic colloidal single particles and dumbbells on a tilted washboard moire pattern in a precessing external field
• Adiabatic and irreversible classical discrete time crystals