标题： 固有（轴子）统计拓扑绝缘体 显示英文标题

标题： Intrinsic (Axion) Statistical Topological Insulator

摘要： 尊重对称性的系综在平均意义上表现出比具有精确对称性的纯态更丰富的拓扑态，这导致了平均对称性保护拓扑态（ASPT）的概念。 ASPT的自由费米子对应物是在无序系综中的所谓统计拓扑绝缘体（STI）。 在本工作中，我们证明了内在STI的存在，它没有清洁对应物。 使用实空间构造（拓扑晶体），我们发现了一个由平均轴子角$\bar{\theta}=\pi$表征的轴子STI，该STI由平均$C_4T$对称性保护，其中$(C_4T)^4=1$。 虽然精确的$C_{4}T$对称性会反转$\theta$角度的符号，因此似乎保护了$\mathbb{Z}_2$分类的$\theta\!=\!0,\pi$，但我们证明如果$(C_{4}T)^4 \!=\! 1$，则$\theta\!=\!\pi$状态在清洁极限下无法实现。因此，轴子 STI 缺乏带绝缘体对应关系，因此是本征的。为了说明这种状态，我们构建了一个格点模型并数值探索其相图，识别出一个由金属相分隔的轴子 STI 相，该金属相既不同于带绝缘体也不同于平凡的安德森绝缘体，揭示了 STI 的本征性质。我们还认为本征 STI 对电子-电子相互作用具有鲁棒性。我们的工作因此提供了第一个本征晶体 ASPT 及其格点实现。 显示英文摘要

摘要： Ensembles that respect symmetries on average exhibit richer topological states than those in pure states with exact symmetries, leading to the concept of average symmetry-protected topological states (ASPTs). The free-fermion counterpart of ASPT is the so-called statistical topological insulator (STI) in disordered ensembles. In this work, we demonstrate the existence of an intrinsic STI, which has no clean counterpart. Using a real space construction (topological crystal), we find an axion STI characterized by the average axion angle $\bar{\theta}=\pi$, protected by an average $C_4T$ symmetry with $(C_4T)^4=1$. While the exact $C_{4}T$ symmetry reverses the sign of $\theta$ angle, and hence seems to protect a $\mathbb{Z}_2$ classification of $\theta\!=\!0,\pi$, we prove that the $\theta\!=\!\pi$ state cannot be realized in the clean limit if $(C_{4}T)^4 \!=\! 1$. Therefore, the axion STI lacks band insulator correspondence and is thus intrinsic. To illustrate this state, we construct a lattice model and numerically explore its phase diagram, identifying an axion STI phase separated from both band insulators and trivial Anderson insulators by a metallic phase, revealing the intrinsic nature of the STI. We also argue that the intrinsic STI is robust against electron-electron interactions. Our work thus provides the first intrinsic crystalline ASPT and its lattice realization.