Robust topological invariants of topological crystalline phases in the presence of impurities,Physical Review B

当前位置： X-MOL 学术 › Phys. Rev. B › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Robust topological invariants of topological crystalline phases in the presence of impurities
Physical Review B ( IF 3.2 ) Pub Date : 2024-07-18 , DOI: 10.1103/physrevb.110.035146
Ian Mondragon-Shem ₁ , Taylor L. Hughes ₂

Affiliation

Topological crystalline phases (TCPs) are topological states protected by spatial symmetries. A broad range of TCPs have been conventionally studied by formulating topological invariants (symmetry indicators) at invariant momenta in the Brillouin zone, which leaves open the question of their stability in the absence of translational invariance. In this work, we show that robust basis-independent topological invariants can be generically constructed for TCPs using projected symmetry operators. Remarkably, we show that the real-space topological markers of these invariants are exponentially localized to the fixed points of the spatial symmetry. As a result, this real-space structure protects them against the presence of impurities that are located away from the fixed points and also sufficiently slowly varying disorder potentials. By considering all possible symmetry centers in a crystalline system we can generate a mesh of real-space topological markers that can provide a local topological distinction for TCPs. We illustrate the robustness of this mesh of invariants with one- and two-dimensional TCPs protected by inversion, rotational, and mirror symmetries. Finally, we find that the boundary modes of these TCPs can also exhibit robust topological invariants with localized markers on the edges. We illustrate this with the gapless Majorana boundary modes of mirror-symmetric topological superconductors, and relate their integer topological edge invariant with a quantized effective edge polarization.

中文翻译：

存在杂质时拓扑晶相的稳健拓扑不变量

拓扑晶相（TCP）是受空间对称性保护的拓扑状态。传统上，通过在布里渊区的不变动量下制定拓扑不变量（对称指标）来研究广泛的 TCP，这留下了在缺乏平移不变性的情况下它们的稳定性问题。在这项工作中，我们证明了可以使用投影对称算子为 TCP 构建鲁棒的独立于基的拓扑不变量。值得注意的是，我们表明这些不变量的实空间拓扑标记呈指数局部化到空间对称性的固定点。因此，这种真实空间结构可以保护它们免受远离固定点的杂质以及足够缓慢变化的无序电位的影响。通过考虑晶体系统中所有可能的对称中心，我们可以生成真实空间拓扑标记的网格，该网格可以为 TCP 提供局部拓扑区别。我们用受反转、旋转和镜像对称保护的一维和二维 TCP 来说明这种不变量网格的鲁棒性。最后，我们发现这些 TCP 的边界模式也可以表现出鲁棒的拓扑不变量，并且边缘上有局部标记。我们用镜像对称拓扑超导体的无间隙马约拉纳边界模式来说明这一点，并将它们的整数拓扑边缘不变量与量化的有效边缘极化联系起来。

更新日期：2024-07-19

点击分享查看原文

点击收藏

公开下载

阅读更多本刊新发论文本刊介绍/投稿指南