Topological crystalline phases in a disordered inversion-symmetric chain
Topological crystalline phases in a disordered inversion-symmetric chain
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DOI：
10.1103/physrevb.103.024205
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发表时间：
2020-07
影响因子：
3.7
通讯作者：
Saavanth Velury;B. Bradlyn;T. Hughes
中科院分区：
文献类型：
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作者：
Saavanth Velury;B. Bradlyn;T. Hughes
当平移对称性被体无序破坏时，拓扑晶体系统中状态的拓扑性质可能会根据所应用的无序类型而改变。在这项工作中，我们刻画了具有反转和手征对称性的一维链的相，其中每个无序构型都是反转对称的。通过使用反转拓扑不变量、手征缠绕数和体极化的与基无关的公式，当无序存在时，我们能够构造这些量的相图。结果表明，与手征缠绕数和体偏振不同，反转拓扑不变量可以随体光谱禁带在强无序状态下的闭合而波动。利用位置-空间重整化群，我们能够比较反转拓扑不变量、手征缠绕数和体极化在强无序极限下的低能行为。结果表明，在保持反转对称性的无序情况下，反转拓扑不变量的值由反转中心态的反转本征值决定，而手征缠绕数和体偏振等量仍然对整个链中的每个态都有贡献。我们还表明，在保持体偏振不变的情况下，通过占据反转中心的附加态，可以改变清洁系统中的反转拓扑不变量的值。我们讨论了我们的结果对高维电子系统中的拓扑晶相的影响，并讨论了在超冷原子系统中潜在的实验实现。
When translational symmetry is broken by bulk disorder, the topological nature of states in topological crystalline systems may change depending on the type of disorder that is applied. In this work, we characterize the phases of a one-dimensional chain with inversion and chiral symmetries, where every disorder configuration is inversion symmetric. By using a basis-independent formulation for the inversion topological invariant, chiral winding number, and bulk polarization, we are able to construct phase diagrams for these quantities when disorder is present. We show that unlike the chiral winding number and bulk polarization, the inversion topological invariant can fluctuate when the bulk spectral gap closes at strong disorder. Using the position-space renormalization group, we are able to compare how the inversion topological invariant, chiral winding number, and bulk polarization behave at low energies in the strong disorder limit. We show that with inversion-symmetry-preserving disorder, the value of the inversion topological invariant is determined by the inversion eigenvalues of the states at the inversion centers, while quantities such as the chiral winding number and the bulk polarization still have contributions from every state throughout the chain. We also show that it is possible to alter the value of the inversion topological invariant in a clean system by occupying additional states at the inversion centers while keeping the bulk polarization fixed. We discuss the implications of our results for topological crystalline phases in higher-dimensional electronic systems, and discuss potential experimental realizations in ultracold-atomic systems.