Topological equivalence of crystal and quasicrystal band structures
Topological equivalence of crystal and quasicrystal band structures
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DOI：
10.1103/physrevb.88.125118
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发表时间：
2013-07
影响因子：
3.7
通讯作者：
Kevin A. Madsen;E. Bergholtz;P. Brouwer
中科院分区：
文献类型：
--
作者：
Kevin A. Madsen;E. Bergholtz;P. Brouwer
最近的一些文章已经报道了在一维无公度晶格模型中存在拓扑上的非平凡态和相关的端态，这通常只在更高的维度上被预期。使用显式结构，我们在这里论证了端态与它们在公度模型中的对应物具有完全相同的起源，并且不可公度性实际上并不提供与高维系统的拓扑分类的有意义的联系。特别地，我们证明了在具有公度和非公度调制参数的状态之间进行平滑内插是可能的，而不需要关闭带隙，也不需要状态穿过带隙。
A number of recent articles have reported the existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an explicit construction, we here argue that the end states have precisely the same origin as their counterparts in commensurate models and that incommensurability does not in fact provide a meaningful connection to the topological classification of systems in higher dimensions. In particular, we show that it is possible to smoothly interpolate between states with commensurate and incommensurate modulation parameters without closing the band gap and without states crossing the band gap.