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Topological tight-binding models from nontrivial square roots

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Topological tight-binding models from nontrivial square roots. / Arkinstall, Jake; Teimourpour, M .H.; Feng, L. et al.
In: Physical review B, Vol. 95, No. 16, 165109, 15.04.2017.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Arkinstall, J, Teimourpour, MH, Feng, L, El-Ganainy, R & Schomerus, H 2017, 'Topological tight-binding models from nontrivial square roots', Physical review B, vol. 95, no. 16, 165109. https://doi.org/10.1103/PhysRevB.95.165109

APA

Arkinstall, J., Teimourpour, M. . H., Feng, L., El-Ganainy, R., & Schomerus, H. (2017). Topological tight-binding models from nontrivial square roots. Physical review B, 95(16), Article 165109. https://doi.org/10.1103/PhysRevB.95.165109

Vancouver

Arkinstall J, Teimourpour MH, Feng L, El-Ganainy R, Schomerus H. Topological tight-binding models from nontrivial square roots. Physical review B. 2017 Apr 15;95(16):165109. Epub 2017 Apr 6. doi: 10.1103/PhysRevB.95.165109

Author

Arkinstall, Jake ; Teimourpour, M .H. ; Feng, L. et al. / Topological tight-binding models from nontrivial square roots. In: Physical review B. 2017 ; Vol. 95, No. 16.

Bibtex

@article{b473ad7da74b4262af3208f5a3753c3f,
title = "Topological tight-binding models from nontrivial square roots",
abstract = "We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial band structure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a nontrivial square root of a parent lattice Hamiltonian—in analogy to the passage from a Klein-Gordon equation to a Dirac equation. In the tight-binding setting, the square-root operation admits to induce spectral symmetries at the expense of broken crystal symmetries. As we illustrate in detail for a simple one-dimensional example, the emergent and inherited spectral symmetries equip the energy gaps with independent topological quantum numbers that control the formation of topologically protected states. We also describe an implementation of this system in silicon photonic structures, outline applications in higher dimensions, and provide a general argument for the origin and nature of the emergent symmetries, which are typically nonsymmorphic.",
author = "Jake Arkinstall and Teimourpour, {M .H.} and L. Feng and R. El-Ganainy and Henning Schomerus",
note = "{\textcopyright}2017 American Physical Society",
year = "2017",
month = apr,
day = "15",
doi = "10.1103/PhysRevB.95.165109",
language = "English",
volume = "95",
journal = "Physical review B",
issn = "1098-0121",
publisher = "AMER PHYSICAL SOC",
number = "16",

}

RIS

TY - JOUR

T1 - Topological tight-binding models from nontrivial square roots

AU - Arkinstall, Jake

AU - Teimourpour, M .H.

AU - Feng, L.

AU - El-Ganainy, R.

AU - Schomerus, Henning

N1 - ©2017 American Physical Society

PY - 2017/4/15

Y1 - 2017/4/15

N2 - We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial band structure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a nontrivial square root of a parent lattice Hamiltonian—in analogy to the passage from a Klein-Gordon equation to a Dirac equation. In the tight-binding setting, the square-root operation admits to induce spectral symmetries at the expense of broken crystal symmetries. As we illustrate in detail for a simple one-dimensional example, the emergent and inherited spectral symmetries equip the energy gaps with independent topological quantum numbers that control the formation of topologically protected states. We also describe an implementation of this system in silicon photonic structures, outline applications in higher dimensions, and provide a general argument for the origin and nature of the emergent symmetries, which are typically nonsymmorphic.

AB - We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial band structure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a nontrivial square root of a parent lattice Hamiltonian—in analogy to the passage from a Klein-Gordon equation to a Dirac equation. In the tight-binding setting, the square-root operation admits to induce spectral symmetries at the expense of broken crystal symmetries. As we illustrate in detail for a simple one-dimensional example, the emergent and inherited spectral symmetries equip the energy gaps with independent topological quantum numbers that control the formation of topologically protected states. We also describe an implementation of this system in silicon photonic structures, outline applications in higher dimensions, and provide a general argument for the origin and nature of the emergent symmetries, which are typically nonsymmorphic.

U2 - 10.1103/PhysRevB.95.165109

DO - 10.1103/PhysRevB.95.165109

M3 - Journal article

VL - 95

JO - Physical review B

JF - Physical review B

SN - 1098-0121

IS - 16

M1 - 165109

ER -