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Rights statement: ©2017 American Physical Society
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -