From an array of quantum wires to three-dimensional fractional topological insulators
From an array of quantum wires to three-dimensional fractional topological insulators
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从量子线阵列到三维分数拓扑绝缘体
DOI：
10.1103/physrevb.92.195137
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发表时间：
2015
影响因子：
3.7
通讯作者：
Y. Oreg
中科院分区：
文献类型：
--
作者：
E. Sagi;Y. Oreg
耦合线方法被证明是描述二维强相互作用拓扑相的有效方法。在这篇手稿中，我们将这种方法扩展到三维，并构造了一个分数强拓扑绝缘体的模型。这种拓扑有序的相在表面有一种奇异的无间隙状态，称为分数狄拉克液体，这是狄拉克自由费米子理论所不能描述的。就像在无相互作用的强拓扑绝缘体中一样，表面受到时间反转对称性和电荷守恒的保护。我们发现，在打破这些对称性之后，有间隙的分数狄拉克液体呈现出独特的特征。特别地，当填充量为$\nu=1/m$时，由时间反转对称性破坏产生的带隙相具有形式为$\sigma_{xy}=\frac{1}{2}\frac{e^{2}}{mh}$的分数霍尔电导减半。另一方面，如果表面与$S波超导体的邻近耦合造成间隙，我们最终得到一个奇异的拓扑超导体。为了揭示这种超导相的拓扑性质，我们将表面划分为两个区域：一个是时间反转对称性破缺的区域，另一个是与超导体耦合的区域。在这两个区域的边界上，我们发现了一个分数Majorana模，它不能用自由Majorana理论来描述。与隧道进入这一一维通道相关的态密度与相应的Laughlin态的边缘成正比。
The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript we extend this approach to three-dimensions, and construct a model for a fractional strong topological insulator. This topologically ordered phase has an exotic gapless state on the surface, called a fractional Dirac liquid, which cannot be described by the Dirac theory of free fermions. Like in non-interacting strong topological insulators, the surface is protected by the presence of time-reversal symmetry and charge conservation. We show that upon breaking these symmetries, the gapped fractional Dirac liquid presents unique features. In particular, the gapped phase that results from breaking time-reversal symmetry has a halved fractional Hall conductance of the form $\sigma_{xy}=\frac{1}{2}\frac{e^{2}}{mh}$ if the filling is $\nu=1/m$. On the other hand, if the surface is gapped by proximity coupling to an $s$-wave superconductor, we end up with an exotic topological superconductor. To reveal the topological nature of this superconducting phase, we partition the surface into two regions: one with broken time-reversal symmetry and another coupled to a superconductor. We find a fractional Majorana mode, which cannot be described by a free Majorana theory, on the boundary between the two regions. The density of states associated with tunneling into this one-dimensional channel is proportional to $\omega^{m-1}$, in analogy to the edge of the corresponding Laughlin state.