Edge states at the boundary between topologically equivalent lattices

TL;DR

This paper investigates edge states of paramagnetic colloidal particles at the boundary of topologically equivalent magnetic lattices, revealing diverse transport modes influenced by symmetry and modulation, challenging traditional bulk-boundary correspondence.

Contribution

It uncovers how edge transport modes depend on symmetry and modulation, demonstrating a variety of behaviors beyond bulk-boundary predictions.

Findings

Edge currents propagate at the boundary between topologically equivalent lattices.

The number of protected modes is not determined by bulk-boundary correspondence.

Edge transport modes vary with symmetry, being ratchet-like or adiabatic, and symmetric or asymmetric.

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.