Topological tight-binding models from nontrivial square roots

Arkinstall, Jake and Teimourpour, M .H. and Feng, L. and El-Ganainy, R. and Schomerus, Henning (2017) Topological tight-binding models from nontrivial square roots. Physical review B, 95 (16): 165109. ISSN 1098-0121

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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.

Item Type:
Journal Article
Journal or Publication Title:
Physical review B
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©2017 American Physical Society
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Deposited On:
24 May 2017 13:08
Last Modified:
09 Jun 2024 23:49