The Su-Schrieffer-Heeger . (SSH) chain is a one-dimensional lattice that comprises two dimerized sublattices. Recently, Zhu, Prodan, and Ahn (ZPA) [Phys. Rev. B 99, 041117(R) (2019)] proposed flat bands can occur at the topological domain walls of two-dimensional array SSH chains. Here, we suggest insulator protected by inversion time-reversal symmetries without spin-orbit coupling. It shown ch...

This book is based on a course given by the author at the university ofLisbon during the academic year 1997–1998. Its aim is to give the readeran idea of how the theory of characteristic classes can be applied to solveindex problems. Starting from the Lefschetz fixed point theorem and itsapplication to the computation of the Euler-Poincaré characteristic of acompact orientab...

This paper is an outgrowth of the notes for a lecture given at the Mathematics Department of Queen’s University in December of 1988. I would like to take this opportunity to thank the members of that department for their hospitality during my visit. I would also like to thank Bruno Kahn for reading early versions of this manuscript and making several helpful remarks. The basic idea of the lectu...