## Topological chiral modes in random scattering networks

Pierre A. L. Delplace

SciPost Phys. 8, 081 (2020) · published 29 May 2020

- doi: 10.21468/SciPostPhys.8.5.081
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### Abstract

Using elementary graph theory, we show the existence of interface chiral modes in random oriented scattering networks and discuss their topological nature. For particular regular networks (e.g. L-lattice, Kagome and triangular networks), an explicit mapping with time-periodically driven (Floquet) tight-binding models is found. In that case, the interface chiral modes are identified as the celebrated anomalous edge states of Floquet topological insulators and their existence is enforced by a symmetry imposed by the associated network. This work thus generalizes these anomalous chiral states beyond Floquet systems, to a class of discrete-time dynamical systems where a periodic driving in time is not required.

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^{1 }Pierre Delplace