Topological Invariant for Bosonic Bogoliubov–de Gennes Systems with Disorder
Topological Invariant for Bosonic Bogoliubov–de Gennes Systems with Disorder
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DOI：
10.7566/jpsj.89.123601
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发表时间：
2020-10
影响因子：
1.7
通讯作者：
Y. Akagi
中科院分区：
文献类型：
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作者：
Y. Akagi
利用非交换几何方法，定义了无序玻色子Bogoliubov-de Gennes系统的拓扑不变量，该系统具有独特的数学性质——非厄米性。为了证明该定义的有效性，我们对二维无序人工自旋冰模型进行了数值研究。在清洁极限下，我们澄清了拓扑指数与陈氏数完全重合。我们还证明了拓扑指数对无序具有鲁棒性。该公式提供了磁振子霍尔域中的拓扑索引$n_{\rm Ch}=1$和平凡局域域中的拓扑索引$n_{\rm Ch}=0$。通过实例表明，该方法可以推广到其他对称类。我们的结果为进一步研究无序拓扑玻色子系统铺平了道路。
Using the method of noncommutative geometry, we define a topological invariant in disordered bosonic Bogoliubov-de Gennes systems, which possess a unique mathematical property---non-Hermiticity. To demonstrate the validity of the definition, we investigate a disordered artificial spin ice model in two dimensions numerically. In the clean limit, we clarify that the topological index perfectly coincides with the Chern number. We also show that the topological index is robust against disorder. The formula provides the topological index $n_{\rm Ch}=1$ in the magnon Hall regime and $n_{\rm Ch}=0$ in a trivial localized one. We also show by example that our method can be extended to other symmetry classes. Our results pave the way for further studies on topological bosonic systems with disorder.