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.
Highlights
We have shown the existence of chiral modes of topological origin in disordered scattering networks
The approach, based on graph theory, allows one to reduce the physical problem of the search for topological modes arising in two-dimensional unitary discrete-time dynamics to the simpler graphical ones assigned to Eulerian graphs, namely, Eulerian circuits, Veblen decompositions and the winding of a graph as defined in this paper
This reduction is motivated by the existence of a strong phase rotation symmetry that emerges in cyclic periodic oriented lattices at specific values of the scattering parameters and that yields anomalous Floquet topological interface states
Summary
Chiral edge states constitute a ubiquitous signature of the topological properties of many physical systems The emergence of such one-way dissipationless modes is well understood in condensed matter with the celebrated bulk-boundary correspondence [1,2,3,4,5,6,7]. This paper is organized as follows: In section 2, we establish a direct mapping between oriented scattering networks and discrete-time periodic tight-binding models introduced in the context of Floquet anomalous topological phases [18, 23] This allows us to represent periodically driven tight-binding models by networks in which we unveil a phase rotation symmetry [34] that imposes the existence anomalous topological chiral states (section 3).
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