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.
3 More- Received 13 October 2016
- Revised 24 February 2017
DOI:https://doi.org/10.1103/PhysRevB.95.165109
©2017 American Physical Society
Physics Subject Headings (PhySH)
Synopsis
The Square Root to Topological States
Published 6 April 2017
A theoretical recipe generates a lattice with topological states by taking the square root of a normal lattice.
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