The Z2 classification of dimensional reduced Hopf insulators

Abstract

Hopf insulators are characterized by a topological invariant called the Hopf index which classifies maps from three-sphere to two-sphere, instead of a Chern number or a Chern parity. In contrast to a topological insulator, the Hopf insulator is not protected by any kind of symmetry. By dimensional reduction, we argue that there exists a new type of index for 2D Hamiltonian with a vanishing Chern number. A specific model Hamiltonian with this nontrivial index is constructed. We also numerically calculate the topological protected edge modes of this dimensional reduced Hopf insulator and show that they are consistent with the classification.