Homotopy theory of strong and weak topological insulators
Homotopy theory of strong and weak topological insulators
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DOI：
10.1103/physrevb.91.245148
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发表时间：
2015-06-23
影响因子：
3.7
通讯作者：
Guggenheim, Charles
中科院分区：
文献类型：
--
作者：
Kennedy, Ricardo;Guggenheim, Charles
我们使用同伦理论将强和弱拓扑绝缘体的概念推广到非稳定区域(占用/空载能带数目较少)。我们证明，要使d维空间中的强拓扑绝缘体是“真正的d维”，即不能通过堆叠低维绝缘体来实现，则需要在稳定区域之外对“强”进行更严格的定义。然而，这并不排除弱的拓扑绝缘体是“真正的d维的”，我们通过一个例子进行了演示。此外，我们还证明了一些有用的技术结果，包括环面上的不变量分解为球面上的稳定区域上的不变量的同伦理论推导，以及对目前文献中广泛使用的参数空间替换T-d->；S-d和T-dk x S-dx->；sdk+dx的严格证明。
We use homotopy theory to extend the notion of strong and weak topological insulators to the nonstable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional," i.e., not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required outside the stable regime. However, this does not exclude weak topological insulators from being "truly d-dimensional," which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of the parameter space replacements T-d -> S-d and T-dk x S-dx -> Sdk+dx used widely in the current literature.