札克相位與繞圈數

Abstract

穩定的邊界態是拓樸絕緣體眾所周知的性質。我們用SSH model 來說明零能量邊界態在任意擾動下的穩定性。此外，已知極化和札克相位成正比。藉由加總各個能帶的札克相位，我們發現即便不存在手徵對稱性，系統的札克相位依然總是2 pi 的整數倍。我們據此建立了札克相位和繞圈數的明確聯繫，並且演示了在沒有手徵對稱性的系統中札克相位和邊界態數量之間的對應關係。

A well known property of topological insulators is the existence of robust edge states. We use the SSH model to illustrate the robustness of the zero energy edge state under arbitrary perturbations. Also, it is known that the polarization is proportional to the Zak phase. By summing over the Zak phase of all the energy bands, the total Zak phase is shown to be always an integer multiple of 2pi even if there is no chiral symmetry. Therefore, we may relate the total Zak phase and the winding number, and we may generalize the bulk-edge correspondence to systems without chiral symmetry.