Topological tight-binding models from nontrivial square roots
Topological tight-binding models from nontrivial square roots
复制标题
DOI：
10.1103/physrevb.95.165109
复制
发表时间：
2017-04-06
影响因子：
3.7
通讯作者：
Schomerus, H.
中科院分区：
文献类型：
--
作者：
Arkinstall, J.;Teimourpour, M. H.;Schomerus, H.
我们描述了一个通用的机制，提供了一个丰富的，拓扑非平凡的带结构紧束缚模型。该机制本质上是代数的，并导致紧束缚模型，可以解释为一个非平凡的平方根的父晶格哈密顿类比的通道从克莱因-戈登方程狄拉克方程。在紧束缚的设置，平方根操作承认诱导光谱对称性的代价破碎的晶体对称性。正如我们在一个简单的一维例子中详细说明的那样，涌现和继承的光谱对称性为能隙配备了独立的拓扑量子数，这些量子数控制着拓扑保护态的形成。我们还描述了该系统在硅光子结构中的实现，概述了在更高维度中的应用，并提供了一个一般的论点的起源和性质的紧急对称性，这是典型的非对称性。
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.