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We prescribe general rules to predict the existence of edge states and zero-energy flat bands in graphene nanoribbons and graphene edges of arbitrary shape. No calculations are needed. For the so-called {it{minimal}} edges, the projection of the edge translation vector into the zigzag direction of graphene uniquely determines the edge bands. By adding extra nodes to minimal edges, arbitrary modified edges can be obtained. The edge bands of modified graphene edges can be found by applying hybridization rules of the extra atoms with the ones belonging to the original edge. Our prescription correctly predicts the localization and degeneracy of the zero-energy bands at one of the graphene sublattices, confirmed by tight-binding and first-principle calculations. It also allows us to qualitatively predict the existence of $E e 0$ bands appearing in the energy gap of certain edges and nanoribbons.
Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional $pi$-magnetism with promising applications in quantum spintronics. A pre
Two-dimensional atomic crystals can radically change their properties in response to external influences such as substrate orientation or strain, resulting in essentially new materials in terms of the electronic structure. A striking example is the c
We study the interplay between the edge states and a single impurity in a zigzag graphene nanoribbon. We use tight-binding exact diagonalization techniques, as well as density functional theory calculations to obtain the eigenvalue spectrum, the eige
An intense laser field in the high-frequency regime drives carriers in graphene nanoribbons (GNRs) out of equilibrium and creates topologically-protected edge states. Using Floquet theory on driven GNRs, we calculate the time evolution of local excit
Carbon-based magnetic structures promise significantly longer coherence times than traditional magnetic materials, which is of fundamental importance for spintronic applications. An elegant way of achieving carbon-based magnetic moments is the design