Three-dimensional network model for strong topological insulator transitions,Physical Review B

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Three-dimensional network model for strong topological insulator transitions
Physical Review B ( IF 3.2 ) Pub Date : 2021-09-27 , DOI: 10.1103/physrevb.104.125142
Jun Ho Son ₁ , S. Raghu _{1,

2}

Affiliation

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. In addition to a weak topological insulator phase already accommodated by the network model framework in the preexisting literature, our network model hosts strong topological insulator phases. We unambiguously demonstrate that strong topological insulator phases emerge as intermediate phases between a trivial insulator phase and a weak topological phase. Additionally, we found a duality that relates a trivial insulator phase and a weak topological phase in our network model. Remarkably, strong topological phases are mapped to themselves under this duality. We show that upon adding sufficiently strong disorder, the strong topological insulator phases undergo phase transitions into a metallic phase. We numerically determine the critical exponent of the insulator-metal transition. Our network model explicitly shows how a semiclassical percolation picture of topological phase transitions in two dimensions can be generalized to 3D and opens up a venue for studying 3D topological phase transitions.

中文翻译：

强拓扑绝缘体跃迁的三维网络模型

我们为整数量子霍尔跃迁构建了 Chalker-Coddington 网络模型的三维 (3D) 时间反转对称推广。除了现有文献中网络模型框架已经容纳的弱拓扑绝缘体相之外，我们的网络模型还包含强拓扑绝缘体相。我们明确地证明，强拓扑绝缘体相作为普通绝缘体相和弱拓扑相之间的中间相出现。此外，我们发现了一个对偶性，它在我们的网络模型中将一个平凡的绝缘体相和一个弱拓扑相联系起来。值得注意的是，在这种二元性下，强拓扑相被映射到自身。我们表明，在添加足够强的无序后，强拓扑绝缘体相经历相变到金属相。我们通过数值确定绝缘体-金属转变的临界指数。我们的网络模型明确地展示了如何将二维拓扑相变的半经典渗透图推广到 3D，并为研究 3D 拓扑相变开辟了一个场所。

更新日期：2021-09-28

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