Localized Electronic States of Graphene on a Substrate with a Terrace-Stepped Sructure

The localized fermionic states arising in an effective field theory model of graphene on the substrate generating a spatially inhomogeneous mass gap were studied. It was shown that in case of terraced-stepped structure of the substrate inhomogeneity in which the chiral mass has the opposite sign on different terraces, both massless and massive fermionic states are generated. The mass spectrum of such states depends on the size of the mass gap generated by the substrate, as well as the width of the terraces, the number of terraces in the substrate structure, and the width of the transition step.