場論在凝態系統應用之研究2

Bulk-edge correspondence is one of the most distinct properties of topological insulators. In particular, the 1-d winding number _x0017_ has a one-to-one correspondence to the number of edge states in a chain of topological insulators with boundaries. By properly choosing the unit cells, we show explicitly in the so-called extended SSH model that the winding numbers corresponding to the left and right unit cells may be used to predict the numbers of edge states on the two boundaries in a _x001C_nite chain. Moreover, by modifying the de_x001C_nition of the Zak phase to be summing over all the bands of the system, we show for a general two-band model that the modi_x001C_ed Zak phase obeys = 2_x0019__x0017_. It is thus always quantized even if there is no chiral symmetry in the system so that it is classi_x001C_ed as trivial in the so-called periodic table of topological materials. We also carry out numerical calculation to demonstrate explicitly that the bulk-edge correspondence may indeed be generalized to this kind of systems.