论文标题
在密度波绝缘子中模拟高阶拓扑绝缘子
Simulating Higher-Order Topological Insulators in Density Wave Insulators
论文作者
论文摘要
自从发现Harper-Hofstadter模型以来，众所周知，具有定期调制的冷凝物质系统可以促进到具有较高维度的新兴仪表领域的非平凡拓扑状态。在这项工作中，我们开发了一种一般程序，以在与具有周期性（电荷和自旋）密度波调制的低维系统相关的较高维度中计算量规场。我们构建具有调制的二维（2D）型号，可以将其促进到3D中的$ U（1）$（1）$（1）$（1）$（1）$（2）$仪表字段。我们的2D模型中的角模式可以通过调制阶段的绝热滑动来泵送，从而在促进的模型中产生铰链模式。我们还检查了由电荷密度波（CDW）阶盖的3D Weyl半学（WSM），具有量子异常的表面状态。我们表明，这个3D系统等于由$ u（1）$ gauge字段与具有非零第二个Chern号码的4D线条系统。我们使用相应的4D理论解释了最近鉴定出的3D WSM的反转对称性阶段的插值。我们的结果可以将较高维度的（高阶）拓扑状态的搜索扩展到密度波系统。
Since the discovery of the Harper-Hofstadter model, it has been known that condensed matter systems with periodic modulations can be promoted to non-trivial topological states with emergent gauge fields in higher dimensions. In this work, we develop a general procedure to compute the gauge fields in higher dimensions associated to low-dimensional systems with periodic (charge- and spin-) density wave modulations. We construct two-dimensional (2D) models with modulations that can be promoted to higher-order topological phases with $U(1)$ and $SU(2)$ gauge fields in 3D. Corner modes in our 2D models can be pumped by adiabatic sliding of the phase of the modulation, yielding hinge modes in the promoted models. We also examine a 3D Weyl semimetal (WSM) gapped by charge-density wave (CDW) order, possessing quantum anomalous Hall (QAH) surface states. We show that this 3D system is equivalent to a 4D nodal line system gapped by a $U(1)$ gauge field with a nonzero second Chern number. We explain the recently identified interpolation between inversion-symmetry protected phases of the 3D WSM gapped by CDWs using the corresponding 4D theory. Our results can extend the search for (higher-order) topological states in higher dimensions to density wave systems.
