Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport

By Miguel Ángel Gracia Bandrés, M. Rechtsman, Mordechai Segev. 2016

239 citations recorded by the source corpus.

We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits scatter-free unidirectional edge states that are extended along the system's perimeter, contrary to the states of an ordinary quasicrystal system, which are characterized by power-law decay. We find that the spectrum of this Floquet topological quasicrystal exhibits a rich fractal (self-similar) structure of topological "minigaps," manifesting an entirely new phenomenon: fractal topological systems. These topological minigaps form only when the system size is sufficiently large because their gapless edge states penetrate deep into the bulk. Hence, the topological structure emerges as a function of the system size, contrary to periodic systems where the topological phase can be completely characterized by the unit cell. We demonstrate the existence of this topological phase both by using a topological index (Bott index) and by studying the unidirectional transport of the gapless edge states and its robustness in the presence of defects. Our specific model is a Penrose lattice of helical optical waveguides - a photonic Floquet quasicrystal; however, we expect this new topological quasicrystal phase to be universal.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/10dc8c8d5ef3746602d8bfd2bbd96500a09fad96

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Highlighting photonics: looking into the next decade (2021, background): “But, as was recently shown, modulation can readily induce a topological gap in structures lacking periodicity altogether, such as quasicrystals [56] or even fractal structures [57].”
Topological photonics (2018, background): “This has led to the experimental realization of intriguing Floquet phases (Rechtsman, Zeuner, Plotnik et al., 2013; Bandres, Rechtsman, and Segev, 2016; Bellec et al., 2017; Noh, Huang, Leykam et al., 2017; Roushan et al., 2017b), in particular, anomalous Floquet topological states (F. Gao et al.,…”