# Edge transport at the boundary between topologically equivalent lattices

H. Massana-Cid , A. Ernst , D. de las Heras , A. Jarosz , M. Urbaniak , F. Stobiecki , A. Tomita , R. Huhnstock , I. Koch , A. Ehresmann , D. Holzinger and T. M. Fischer

Soft Matter, **15**, 1539, (2019) DOI: 10.1039/C8SM02005A

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**Abstract**:

Edge currents of paramagnetic colloidal particles propagate at the edge between two topologically equivalent magnetic lattices of different lattice constant when th esystem 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, time or non-time reversal symmetric. The topological nature of the edge transport is classified by a set of winding numbers around bulk fence points extended by winding numbers around edge specific bifurcation points that cannot be deduced from the two bulk lattices.

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