Topological insulator phases and zero-line channels in graphene

Topological phases can be induced in single and bilayer graphene in the presence of appropriate spin-orbit coupling and external potentials. We survey the character of the different metallic 1D zero line channels at bulk-vacuum edges and at interfaces between regions with different bulk topological order in single and bilayer graphene. We use a tight-binding Hamiltonian for ribbon geometries to study the character of the 1D zero-line channels appearing at the interfaces between regions of different topological phases. Depending on the resulting states, the number of 1D metallic channels at interface and edge differ that these can be thought as a characterization of the states.