Observation of a Higher-Order Topological Bound State in the Continuum

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Observation of a Higher-Order Topological Bound State in the Continuum

Alexander Cerjan, Marius Jürgensen, Wladimir A. Benalcazar, Sebabrata Mukherjee, and Mikael C. Rechtsman

Phys. Rev. Lett. 125, 213901 – Published 17 November 2020

Abstract

Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the system. Here, we experimentally demonstrate that the topological corner-localized modes of higher-order topological systems can be symmetry-protected bound states in the continuum; these states do not hybridize with the surrounding bulk states of the lattice even in the absence of a bulk band gap. This observation expands the scope of bulk-boundary correspondence by showing that protected boundary-localized states can be found within topological bands, in addition to being found in between them.

Received 27 June 2020
Accepted 13 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.213901

Physics Subject Headings (PhySH)

Photonic crystals Photonics Topological effects in photonic systems Topological insulators

Topological materials

Atomic, Molecular & Optical

Authors & Affiliations

Alexander Cerjan ^*, Marius Jürgensen , Wladimir A. Benalcazar ^†, Sebabrata Mukherjee , and Mikael C. Rechtsman ^‡

Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

^*awc19@psu.edu
^†wxb151@psu.edu
^‡mcrworld@psu.edu

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Vol. 125, Iss. 21 — 20 November 2020

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Images

Figure 1
(a) Schematic of a higher-order topological waveguide array. A unit cell is marked with a black dashed square. (b) Density of states (top panel) and associated local density of states (bottom panel) for each band of a finite lattice, calculated using the tight-binding approximation. (c) Bulk band structure for the higher-order topological waveguide array, calculated using full-wave numerical simulations for $λ = 850 nm$ , $l_{intra} = 17 μ m$ , and $l_{inter} = 13 μ m$ . (d) White light transmission micrograph of the output facet of a waveguide array, with $l_{intra} = 13 μ m$ and $l_{inter} = 11 μ m$ . An auxiliary waveguide into which light can be injected is indicated with a black arrow.
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Figure 2
(a) Schematic of a waveguide array with the boundary of the “subsystem” for $n_{s} = 3$ indicated. (b),(c) Experimentally observed (b) and numerically simulated (c) fractional power, as a function of the size of the subsystem, $n_{s}$ , and the spacing between adjacent waveguides within the same unit cell, $l_{intra}$ . We fix $l_{inter} = 13 μ m$ , and use $λ = 850 nm$ , with a propagation distance of $L = 7.6 cm$ . The arrays consist of $9 \times 9$ unit cells. The topological transition is denoted in green at $l_{intra} = l_{inter} = 13 μ m$ . (d),(e) Experimentally observed intensity for $l_{intra} = 17 μ m$ (d) and $l_{intra} = 9 μ m$ (e). Light is injected into the leftmost waveguide at the corner of the array, marked with a white arrow. (f),(g) The same as (d),(e), except for full wave numerical simulations of the waveguide array. (h) Experimentally observed intensity for a topological array, with $l_{intra} = 13 μ m$ and $l_{inter} = 11 μ m$ , with wavelength $λ = 900 nm$ and propagation distance $L = 7.6 cm$ . Light is injected using an auxiliary waveguide placed $20 μ m$ away from the corner of the lattice (marked with a white arrow). (i) The same as (h) except with $l_{intra} = 11 μ m$ and $l_{inter} = 13 μ m$ .
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Figure 3
(a) Schematic of a higher-order topological waveguide array with broken chiral symmetry, with an auxiliary waveguide $20 μ m$ away from the array. Green colored waveguides were fabricated using slower writing speeds, resulting in a larger refractive index (decreased on-site energy). (b) Bulk band structure for the higher-order topological array with broken chiral symmetry, calculated using full-wave numerical simulations for $λ = 900 nm$ , $l_{intra} = 13 μ m$ , and $l_{inter} = 11 μ m$ , corresponding to the results shown in (f), below [71]. (c) Density of states (top panel) and associated local density of states for each band (bottom panel) for a tight-binding lattice with broken chiral symmetry. Zero energy of the chiral symmetric array is marked. (d) Experimentally observed intensity of the chiral symmetric array consisting of $9 \times 9$ unit cells, with $l_{intra} = 13 μ m$ , $l_{inter} = 11 μ m$ , and $λ = 900 nm$ , and propagation distance $L = 7.6 cm$ . The auxiliary waveguide where light is injected is marked with a white arrow. (e)–(h) Similar to (d), except with increasing the refractive index of the indicated sublattice of the array [71].
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