Co-existing topological and Volkov-Pankratov plasmonic edge states in magnetized graphene

Graphene placed in a perpendicular magnetic field supports optical modes known as magnetoplasmons which are transversally confined to the graphene layer. Unlike ordinary graphene plasmons, these magnetoplasmonic surface waves are characterized by a band gap corresponding to the cyclotron frequency. In addition, these magnetoplasmon bands are topological, characterized by a non-zero Chern number. This leads to the existence of topologically protected edge states at domain edges where the Chern number changes. Since the Chern number is dependent on the direction of the magnetic field, edge states exist at domain edges across which the magnetic field flips direction. Physically, the magnetic field can only flip direction at gradual domain edges with finite width creating topological heterojunctions. These topological heterojunctions support extra edge states known as Volkov-Pankratov edge states which can enter the band gap and support propagation in both directions. The number of Volkov-Pankratov states at a heterojunction varies as a function of the width of the gradual domain edge.