Connection between the winding number and the Chern number

• DOI: 10.48550/arxiv.1908.06700
• Publication Date: 2019-01-01
• Authors: Han‐Ting Chen; Chia‐Hsun Chang; Hsien-Chung Kao
• Keywords: Winding number; Brillouin zone; Chain (unit); Momentum (technical analysis)

Bulk-edge correspondence is one of the most distinct properties topological insulators. In particular, 1D winding number $\n$ has a one-to-one to edge states in chain insulators with boundaries. By properly choosing unit cells, we carry out numerical calculation show explicitly extended SSH model that numbers corresponding left and right cells may be used predict on two boundaries finite chain. Moreover, by drawing analogy between QWZ model, generalized model. integrating ``magnetic field'' over momentum strip $0\le p_2 \le \pi, 0\le p_1 2\pi$ Brillouin zone, identity relating 2D Chern difference at $p_2=0 $ $p_2 =\pi$.