Boundaries of boundaries: A systematic approach to lattice models with solvable boundary states of arbitrary codimension

Kunst, Flore K.; Miert, Guido van; Bergholtz, Emil J.

doi:10.1103/physrevb.99.085426

Cited by 27 publications

(45 citation statements)

References 74 publications

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“…where a † A,m,m creates a state on the A sublattice (red in Fig. 1(a)) in the unitcell numbered by (m, m ) starting with (0, 0) at the lower left corner [17,28]. In addition to the corner localisation, a second striking feature of this state is that it resides on the (red) A sublattice.…”

Section: Breathing Kagome Lattice Of Lightmentioning

confidence: 98%

Corner states of light in photonic waveguides

Hassan¹,

Kunst²,

Moritz³

et al. 2019

Nat. Photonics

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427

244

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The recently established paradigm of higher-order topological states of matter has shown that not only, as previously thought, edge and surface states but also states localised to corners can have robust and exotic properties. Here we report on the experimental realisation of novel corner states made out of classical light in three-dimensional photonic structures inscribed in glass samples using femtosecond (fs) laser technology. By creating and analysing waveguide arrays forming two-dimensional breathing kagome lattices in various sample geometries, we establish this as a platform for corner states exhibiting a remarkable degree of flexibility and control. In each sample geometry we measure eigenmodes that are localised at the corners in a finite frequency range in complete analogy with a theoretical model of the breathing kagome. Here, the measurements reveal that light can be "fractionalised", corresponding to simultaneous localisation to each corner of a triangular sample, even in the presence of defects. The fabrication method applied in this work exposes the advantage of using fs-laser writing for producing compact three-dimensional devices thus paving the way for technological applications by simulating novel higher-order states of matter. arXiv:1812.08185v3 [cond-mat.mes-hall]

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Section: Breathing Kagome Lattice Of Lightmentioning

confidence: 98%

Corner states of light in photonic waveguides

Hassan¹,

Kunst²,

Moritz³

et al. 2019

Nat. Photonics

Self Cite

427

244

View full text Add to dashboard Cite

show abstract

“…Remarkably, these models host zero-dimensional corner modes under the open boundary conditions in all directions, which coincide with the quantization of the bulk multipole moment under the periodic boundary conditions. This kind of HOTI states was also found in breathing kagome and pyrochlore lattices [22][23][24][25]. Together with these theoretical developments, experimental realization of the HOTIs has also been intensively pursued both in solid-state systems [26] and artificial materials [27][28][29][30].…”

mentioning

confidence: 96%

“…Since the adiabatic connection to the irreducible cluster state is a ubiquitous property of the SPT phases, the characterization of the HOSPT phases by the Z Q Berry phase can applicable to wide class of models beyond the square-lattice models, such as the breathing kagome/pyrochlore models [44,51] Recently, it is found that the breathing kagome model and breathing Pyrochlore model have the higher-order topological insulator (HOTI) phase [22,24]. In the HOTI phases, the models have mid-gap corner states, which is exactly solvable with certain boundary conditions [23,25]. In this section, we show the correspondence between the Z Q Berry phases and the HOTI phases in the breathing kagome model and the breathing Pyrochlore model.…”

mentioning

confidence: 99%

ZQ Berry phase for higher-order symmetry-protected topological phases

Araki

Mizoguchi

Hatsugai

2020

Phys. Rev. Research

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We propose the ZQ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in Z4 and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest neighbor hopping and the intersite Coulomb interactions. Furthermore, we introduce the Z4 Berry phase for the spin-model-analog of the BBH model, whose topological invariant has not been found so far. We also confirm the bulk-corner correspondence between the Z4 Berry phase and the corner states in the HOSPT phases.

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“…From Eqs. (33) and (34), one finds that the energy eigenvalue ε L (k y ) has to be determined such that…”

Section: Dispersion Relation Of Edge Modementioning

confidence: 99%

Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models

2020

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Detecting chiral edge modes in topological materials has been intensively pursued in experiments. However, the phenomena caused by the modes are not yet elucidated theoretically. We study the dynamics of chiral spinon wave packets at the edge in Kitaev-type magnets. More precisely, by relying on the exact solvability of the models, we construct a spinon wave packet, localized edge magnetization, which shows oriented propagation along the edge, whose behavior is expected from the chiral character of the dispersion relation of the chiral edge modes. In general, this approach enables us to study not only spin transport in anisotropic magnets but also charge transport in Bogoliubov-de Gennes-type superconductors because it does not rely on a conserved quantity.

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Boundaries of boundaries: A systematic approach to lattice models with solvable boundary states of arbitrary codimension

Cited by 27 publications

References 74 publications

Corner states of light in photonic waveguides

Corner states of light in photonic waveguides

ZQ Berry phase for higher-order symmetry-protected topological phases

Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models

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