| Abstract: | The tenfold classification of insulators and superconductors allows to identify possible topological phases but a systematic approach to construct topological materials is missing. We present a new description (the symbol of a Hamiltonian) which contains all relevant topological information about the system and which allows to modify its properties so as to navigate across the tenfold classification and construct new topological materials. Monolayer and multilayer graphene with defects serve as useful examples. |