[论文解读] Topological phase transitions for any taste in 2D quasiperiodic systems

Tiago S. Gonçalves, Miguel Gonçalves+2 more|arXiv (Cornell University)|Dec 15, 2022

Topological Materials and Phenomena被引用 4

一句话总结

本文通过精确数值方法研究了二维准周期陈绝缘体中的拓扑相变，揭示了在纯净或无序系统中未见的丰富相变类型。结果表明，准周期性可驱动能隙关闭与重开，导致出现新相，包括临界态以及能隙边缘的弹道-局域化相变，其拓扑相变在纯净或未关联无序系统中均无对应现象。

ABSTRACT

In this paper we explore the effects of quasiperiodicity in paradigmatic models of Chern insulators. We identify a plethora of topological phase transitions and characterize them based on spectral and localization properties. Contrary to uncorrelated disorder, gap closing and reopening topological transitions can be induced by quasiperiodicity. These can separate widely different phases, including (i) trivial and Chern insulators, both with ballistic states near the gap edges; (ii) Chern insulators with critical states around the gap edges or (iii) Chern and trivial insulators respectively with ballistic and localized gap-edge states. Transition (i) is similar to clean-limit topological transitions due to the ballistic character of the gap-edge states, but at the same time resembles (quasi)disorder driven topological Anderson insulator phenomena. On the other hand, transitions (ii) and (iii) have no clean-limit counterpart. Additionally, quasiperiodicity can also induce topological transitions into a trivial state for which the gap closes and does not reopen, a scenario that resembles more what is observed with uncorrelated disorder. However, we found that such transitions can also be non-conventional in that they can be accompanied by the emergence of intermediate metallic and critical phases where the Chern number is not quantized. Our results show that a rich variety of topological phase transitions, not previously realized experimentally nor predicted theoretically can be attained when applying quasiperiodic modulations to simple Chern insulators. Such models have previously been realized experimentally in widely different platforms, including in optical lattices and photonic or acoustic media, where quasiperiodicity effects can be incorporated. The unveiled topological phase transitions can in principle be observed experimentally with state-of-the-art techniques.

研究动机与目标

• 探究准周期势对典型陈绝缘体模型（如Haldane模型和BHZ模型）的影响。
• 识别并分类由准周期性诱导的新类型拓扑相变，特别是那些在纯净或无序系统中不存在的相变。
• 表征能隙边缘处拓扑性、能谱性质与局域化（弹道、局域、临界）之间的相互作用。
• 确定准周期性是否可驱动进入非重开能隙的 trivial 相，其行为类似于无序但具有非典型特征。
• 评估在光学晶格、光子学与声学平台中观测这些相变的实验可行性。

提出的方法

• 采用精确数值方法，包括有限尺寸标度与热力学极限外推，计算能谱间隙与局域化性质。
• 利用局域化程度的倒数（IPR）与动量空间IPR（IPR_k）对本征态局域化进行分类：弹道（IPR ~ 1/N）、局域（IPR ~ 1）或临界（IPR ~ N^(-0.5)）。
• 通过Fukui-Hughes-Asahara方法计算陈数，以识别拓扑相并检测相变。
• 分析不同系统尺寸下能谱间隙的演化，并应用线性回归估计热力学极限。
• 对200个准周期构型进行系综平均，以确保统计稳健性。
• 通过陈数的不连续性、能隙关闭/重开以及局域化行为的变化来识别相变。

实验结果

研究问题

• RQ1 准周期势是否能诱导能谱间隙关闭与重开的拓扑相变，而这种现象在未关联无序系统中不会出现？
• RQ2 在二维准周期陈绝缘体中，哪些类型的拓扑相变出现，且在纯净或无序系统中均无对应？
• RQ3 在不同拓扑相变过程中，能隙边缘态的局域化性质（弹道、临界、局域）如何演化？
• RQ4 准周期性是否可驱动从陈绝缘体到具有中间金属相与临界相的 trivial 无能隙安德森绝缘体的相变？
• RQ5 在由准周期性诱导的拓扑相变过程中，是否存在中间相中陈数未被量化的情况？

主要发现

• 在Haldane模型的准周期势下识别出三种不同的拓扑相变：分别位于V ≈ 1.007t、1.95t与2.435t处，前两种涉及能隙关闭与重开。
• 相变(i)在 trivial 与陈绝缘体之间发生，其能隙边缘具有弹道态，类似于纯净极限下的相变，但表现出类似无序的局域化效应。
• 相变(ii)在陈绝缘体之间发生，其能隙边缘出现临界态，这种现象在纯净系统与未关联无序系统中均不存在。
• 相变(iii)表现为能隙边缘态从弹道到局域化的转变，陈数由非零变为零，且无能隙重开。
• 观察到一种新型相变，进入 trivial 无能隙安德森绝缘体相，其间存在金属相与临界相，且陈数未被量化。
• 未发现具有在费米能级局域态的无能隙拓扑绝缘相——这与未关联无序系统中的情况不同——凸显了准周期系统的关键差异。