Kaleidoscopes of Hofstadter butterflies and Aharonov-Bohm caging from 
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-root topology in decorated square lattices

Marques, A. M.; Mögerle, J.; Pelegrí, G.; Flannigan, Stuart; Dias, R. G.; Daley, Andrew J.

doi:10.1103/physrevresearch.5.023110

“…1(a)). In the case of extended Lieb lattices [9][10][11] , the nodes from minority form chains: dimmers, trimmers, etc. (Fig.…”

Section: Introductionmentioning

confidence: 99%

Compact localised states in magnonic Lieb lattices

Kłos

¹

,

Centała

²

2023

Preprint

0

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Lieb lattice is one of the simplest bipartite lattices, where compact localized states (CLS) are observed. This type of localization is induced by the peculiar topology of the unit cell, where the modes are localized only on selected sublattices due to the destructive interference of partial waves. We demonstrate the possibility of magnonic Lieb lattice realization, where flat bands and CLS can be observed in the planar structure of sub-micron in-plane sizes. Using forward volume configuration, the Ga-doped YIG layer with cylindrical inclusions (without Ga content) arranged in a Lieb lattice with 250 nm period was investigated numerically (finite-element method). The structure was tailored to observe, for a lowest magnonic bands, the oscillatory and evanescent spin waves in inclusions and matrix, respectively. Such a design reproduces the Lieb lattice of nodes (inclusions) coupled to each other by the matrix with the CLS in flat bands.

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Photonic Square‐Root Second‐Order Topological Bound States in the Continuum

Yan,

Cheng,

Liu

et al. 2024

Laser & Photonics Reviews

1

0

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Second‐order topological bound states in the continuum (SOTBICs) have received widely attention in photonics due to theirs counterintuitive localized properties. A model of square‐root SOTBICs is proposed that not only inherit topological features from its parent Hamiltonian, but also support multiple corner states with different propagation constants, a unique feature not found in its parent Hamiltonian. Using femtosecond laser‐writing technology, a photonic nontrivial 2D edge‐centered SSH lattice is fabricated and observe two types of localized corner states with distinct phase distribution. Interestingly, by using an auxiliary waveguide with defined refractive index and coupling into the array, it is experimentally demonstrated that corner states are embedded but do not hybridize with bulk states of the lattice. Additionally, it is experimentally verified that these square‐root SOTBICs are robust against disorders as long as the essential symmetries remain preserved. The work marks the instance of SOTBICs with multiple corner states in photonic lattices.

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Compact localized states in magnonic Lieb lattices

Centała

¹

,

Kłos

²

2023

Sci Rep

2

0

View full text Add to dashboard Cite

Lieb lattice is one of the simplest bipartite lattices, where compact localized states (CLS) are observed. This type of localization is induced by the peculiar topology of the unit cell, where the modes are localized only on selected sublattices due to the destructive interference of partial waves. We demonstrate the possibility of magnonic Lieb lattice realization, where flat bands and CLS can be observed in the planar structure of sub-micron in-plane sizes. Using forward volume configuration, the Ga-doped YIG layer with cylindrical inclusions (without Ga content) arranged in a Lieb lattice with 250 nm period was investigated numerically (finite-element method). The structure was tailored to observe, for a lowest magnonic bands, the oscillatory and evanescent spin waves in inclusions and matrix, respectively. Such a design reproduces the Lieb lattice of nodes (inclusions) coupled to each other by the matrix with the CLS in flat bands.

show abstract

Kaleidoscopes of Hofstadter butterflies and Aharonov-Bohm caging from 2n -root topology in decorated square lattices

Cited by 9 publications

References 109 publications

Compact localised states in magnonic Lieb lattices

Compact localised states in magnonic Lieb lattices

Photonic Square‐Root Second‐Order Topological Bound States in the Continuum

Compact localized states in magnonic Lieb lattices

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