Corner modes of the breathing kagome lattice: Origin and robustness

Herrera, Marcela; Kempkes, S. N.; Paz, María Blanco de; García‐Etxarri, Aitzol; Swart, Ingmar; Smith, C. Morais; Bercioux, Dario

doi:10.1103/physrevb.105.085411

Cited by 26 publications

(22 citation statements)

References 65 publications

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“…This symmetry is the same that features the breathing Kagome lattice [33]. However, due to the absence of the C 3 rotational symmetry also present in the Kagome lattice, in this 1D system there are no three degenerate zerostates but non-zero edge states.…”

Section: A Extended Unit Cell Ssh Modelsmentioning

confidence: 64%

Exploiting oriented field projectors to open topological gaps in plasmonic nanoparticle arrays

Buendía¹,

Sánchez‐Gil²,

Giannini³

2022

Preprint

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In the last years there have been multiple proposals in nanophotonics to mimic topological condensed matter systems. However, nanoparticles have degrees of freedom that atoms lack of, like dimensions or shape, which can be exploited to explore topology beyond electronics. Elongated nanoparticles can act like projectors of the electric field in the direction of the major axis. Then, by orienting them in an array the coupling between them can be tuned, allowing to open a gap in an otherwise gapless system. As a proof of the potential of the use of orientation of nanoparticles for topology, we study 1D chains of prolate spheroidal silver nanoparticles. We show that in these arrays spatial modulation of the polarization allows to open gaps, engineer hidden crystalline symmetries and to switch on/off or left/right edge states depending on the polarization of the incident electric field. This opens a path towards exploiting features of nanoparticles for topology to go beyond analogues of condensed matter systems.

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Section: A Extended Unit Cell Ssh Modelsmentioning

confidence: 64%

Exploiting oriented field projectors to open topological gaps in plasmonic nanoparticle arrays

Buendía¹,

Sánchez‐Gil²,

Giannini³

2022

Preprint

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“…As a representative example, we considered kagome lattice demonstrating topological edge and corner states experimentally. Recent studies [ 39–41 ] argue that the corner states in kagome lattice arise due to the nontrivial edge polarization rather than the bulk properties and hence do not have higher‐order topological origin (see Supporting Information for further details). However, our approach is general and can be applied to the other types of lattices, for example, those with C 6 symmetry, enabling truly higher‐order topological phases with vanishing bulk polarization.…”

Section: Discussionmentioning

confidence: 99%

Topological Edge and Corner States Designed via Meta‐Atoms Orientation

Bobylev

Tikhonenko

Zhirihin

et al. 2022

Laser & Photonics Reviews

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Rapid development of topological concepts in photonics unveils exotic phenomena such as unidirectional propagation of electromagnetic waves resilient to backscattering at sharp bends and disorder‐immune localization of light at stable frequencies. Recently introduced higher‐order topological insulators (HOTIs) bring in additional degrees of control over light confinement and steering. However, designs of photonic HOTIs reported so far are solely exploiting lattice geometries which are hard to reconfigure thus limiting tunability. This article reports a conceptually new mechanism to engineer topological edge and corner states including higher‐order topological phases which exploits both electric and magnetic responses of the meta‐atoms. Hybridization between these responses gives rise to the difference in the effective coupling which is controlled by the meta‐atoms mutual orientations. This feature allows to tailor photonic band topology exclusively via particle alignment and flexibly reconfigure the topological phase. Focusing on the kagome array of split‐ring resonators, the topological edge and corner states are experimentally demonstrated in the microwave domain. To highlight the generality of this proposal, the formation of higher‐order topological phase is also predicted numerically in a C6‐symmetric lattice of split‐ring resonators. These findings provide a new promising route to induce and control higher‐order topological phases and states.

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“…The HL can be realized within a synthetic platform based on the electron simulator, where CO molecules are placed on top of the Cu(111) surface [27,28,[38][39][40][41][42][43]. A possible design of this lattice is presented in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…Among the electron simulators, specific technique describes a particular class of experiments of atomic manipulation [27,28,30,38,44,45]. Here [28], a twodimensional electron gas is hosted on the (111) surface state of Cu, and it is decorated with a set of CO molecules placed with atomic precision at certain positions, with the help of the tip of a scanning tunnelling microscope [30].…”

Section: S5 Synthetic Matter As a Platformmentioning

confidence: 99%

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Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice

Herrera¹,

Bercioux²

2022

Preprint

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We investigate the spectral properties of a two-dimensional electronic lattice belonging to a nonsymmorphic wallpaper group. Specifically, we look at the herringbone lattice, characterised by two sets of glide symmetries applied in two orthogonal directions. We describe the system using a nearest-neighbour tight-binding model containing horizontal and vertical hopping terms. We find two non-equivalent Dirac cones inside the first Brillouin zone along a high-symmetry path. Among other features, these Dirac cones can be tuned via different perturbations applied to the Hamiltonian. These perturbations break the symmetries of the lattice: we begin by placing different onsite potentials in the lattice sites. We observe the annihilation of Dirac cones into semi-Dirac cones and nodal lines along high-symmetry paths. Finally, we perturb the system by applying a dimerization of the hopping terms. We report a flow of Dirac cones inside the first Brillouin zone describing quasi-hyperbolic curves. We present, as well, a possible implementation in terms of CO atoms placed on the top of a Cu(111) surface.

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Corner modes of the breathing kagome lattice: Origin and robustness

Abstract: √ 3 2 ) and a 3 = a 2 − a 1 = (−1, 0) the lattice vectors. The Hamiltonian (1) is expressed in the basis = {ψ A , ψ B , ψ C } T , where T represents the transposition. We show in Fig. 1(b) the band structure for a periodic lattice 085411-2

Cited by 26 publications

References 65 publications

Exploiting oriented field projectors to open topological gaps in plasmonic nanoparticle arrays

Exploiting oriented field projectors to open topological gaps in plasmonic nanoparticle arrays

Topological Edge and Corner States Designed via Meta‐Atoms Orientation

Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice

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