無義拓樸中之穩定保護無隙邊緣態

Abstract

拓樸絕緣體是一種具有整體性拓樸或邊界性異常的一系列材料。其中，整體-邊界對應關係是拓樸絕緣體中很重要的特徵，包括陳絕緣體和Z2拓樸絕緣體。這些拓樸絕緣體具有威爾森迴圈光譜環繞的特性，並且無法被構造出對稱局域萬尼爾函數。然而，最近的研究指出這些整體性拓樸特徵並不一定能反映出邊界的保護無隙態。本論文第一個提出穩定保護邊界態也可以在沒有前述整體性拓樸的情況下出現。我們發現這些「無義拓樸絕緣體」具有穩定的多胞性拓樸。特別地是，本論文模型中的穩定保護無隙態並不是被晶體對稱性保護而是被鏡像反對稱給保護。另外，我們也給出了拓樸不變量以及確認了糾纏光譜中的環繞。本論文因此得到了即使原子絕緣體也可以有穩定無隙邊界態的結論。

Topological insulator is a class of materials that exhibits nontrivial bulk topology or boundary anomalies. The associated bulk-boundary correspondence serves as an important feature of topological insulators, including Chern insulators and Z2 topological insulators. These topological insulators have spectral flow in the Wilson-loop spectrum and encounter Wannier obstruction. However, recent studies show that the bulk topological features may not imply the existence of protected gapless boundary states. In this thesis, we first provide an example where the stably protected gapless edge states arise without the aforementioned bulk topological features. We show that this "trivialized topological insulator" belongs to the first example of systems with stable multicellularity and non-delta like Wannier functions. The gapless edge states in the model are not protected by the crystalline symmetry but the mirror antisymmetry. In addition, we identify the associated topological invariant and the spectral flow in the entanglement spectrum. This thesis thus clarifies that even the atomic insulators can host stably protected gapless edge states.