Helical bound states in the continuum of the edge states in two dimensional topological insulators

Sablikov, V. A.; Sukhanov, Aleksei A.

doi:10.1016/j.physleta.2015.05.005

Cited by 21 publications

(12 citation statements)

References 18 publications

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“…More recently, Friedrich-Wintgen BICs have been studied in continuum shell models 121 , cold-atom collisions 122 , 2D topological insulators with defect 123 , and for quantum graphs 124 , quantum billiards 125 , or impurity atoms 126,127 attached to leads. In acoustics they have been studied in multi-resonant cavities 103,128 .…”

Section: Friedrich-wintgen Bic (Through Coupled Resonances)mentioning

confidence: 99%

Bound states in the continuum

et al. 2016

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Bound states in the continuum are waves that, defying conventional wisdom, remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their existence was first proposed in quantum mechanics and, being a general wave phenomenon, later identified in electromagnetic, acoustic, and water waves. They have been studied in a wide variety of material systems such as photonic crystals, optical waveguides and fibers, piezoelectric materials, quantum dots, graphene, and topological insulators. This Review describes recent developments in this field with an emphasis on the physical mechanisms that lead to these unusual states across the seemingly very different platforms. We discuss recent experimental realizations, existing applications, and directions for future work.

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Section: Friedrich-wintgen Bic (Through Coupled Resonances)mentioning

confidence: 99%

Bound states in the continuum

et al. 2016

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“…III B, we start with Eqs. (22) and (23). Because these equations must have the same eigenvalue and eigenstate, there are two distinct cases:…”

Section: Appendix A: Details Of Calculations On the Energy And The Lo...mentioning

confidence: 99%

“…These states are called bound states in the continuum (BIC) [1]. They have been proposed in many different fields such as photonics [2][3][4][5][6][7][8][9][10][11][12][13][14][15], acoustics [16][17][18], and electronics [19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Topological linelike bound states in the continuum

Takeichi

Murakami

2019

Phys. Rev. B

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Bound states in the continuum (BIC) have been studied mainly in optics. Recently, electronic BIC have been proposed. They appear as points in the momentum space and are protected topologically by the Chern number. In this study, we propose a type of BIC protected by the winding number, which is one of the topological invariants. These BIC appear as lines in the momentum space, and are realized in a multilayer model consisting of honeycomb-lattice layers. We show band structure and spatial localization of the BIC in this model. The wave numbers at which the BIC appear can be explained in terms of topology in the momentum space. arXiv:1810.08154v2 [cond-mat.mes-hall]

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“…Special interest deserves the development of such states in materials, ranging from photonics to quantum dots in a plethora of different setups and aiming for technological applications (see [14] for a review). BICs have also been studied in graphene [21], some topologically insulating materials [22] and, from the formal point of view, modeling the Dirac equation in curved space [23]. A common denominator in these cases is the static character of the effective potential in the effective wave equation governing the underlying system.…”

Section: Introductionmentioning

confidence: 99%

Freezable bound states in the continuum for time-dependent quantum potentials

Altamirano,

Contreras-Astorga,

Raya

2021

Preprint

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In this work, we construct time-dependent potentials for the Schrödinger equation via supersymmetric quantum mechanics. The generated potentials have a quantum state with the property that after a particular threshold time t F , when the potential does no longer change, the evolving state becomes a bound state in the continuum, its probability distribution freezes. After the factorization of a geometric phase, the state satisfies a stationary Schrödinger equation with time-independent potential. The procedure can be extended to support more than one bound state in the continuum. Closed expressions for the potential, the bound states in the continuum, and scattering states are given for the examples starting from the free particle.

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Helical bound states in the continuum of the edge states in two dimensional topological insulators

Cited by 21 publications

References 18 publications

Bound states in the continuum

Bound states in the continuum

Topological linelike bound states in the continuum

Freezable bound states in the continuum for time-dependent quantum potentials

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