SciPost Physics

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.

• De Beule et al., Effective Floquet model for minimally twisted bilayer graphene
  Phys. Rev. B 103, 195432 (2021) [Crossref]
• Upreti et al., Topological chiral interface states beyond insulators
  Phys. Rev. A 102, 023520 (2020) [Crossref]
• Upreti et al., Topological Swing of Bloch Oscillations in Quantum Walks
  Phys. Rev. Lett. 125, 186804 (2020) [Crossref]
• Chen et al., Anomalous and Chern topological waves in hyperbolic networks
  Nat Commun 15, 2293 (2024) [Crossref]
• Zhang et al., Superior robustness of anomalous non-reciprocal topological edge states
  Nature 598, 293 (2021) [Crossref]
• Potter et al., Quantum Hall Network Models as Floquet Topological Insulators
  Phys. Rev. Lett. 125, 086601 (2020) [Crossref]
• Zhang et al., Anomalous topological waves in strongly amorphous scattering networks
  Sci. Adv. 9, eadg3186 (2023) [Crossref]
• De Beule et al., Network model for periodically strained graphene
  Phys. Rev. B 107, 045405 (2023) [Crossref]
• Zhang et al.,
  , 1 (2023) [Crossref]