Graphene provides an ideal table-top test-ground for relativistic physics due to the Dirac-type linear dispersion of electrons of carbon atoms. Haldane and Kane and Mele discovered that, taking into account the hopping between next-nearest-neighbor carbon atoms, one can achieve topological electronic states known as quantum anomalous Hall effect and quantum spin Hall effect . Recently we have found that introducing superstructures respecting C6v crystalline symmetry into graphene will also generate topological states [2-6], without resort to staggered flux and/or spin-orbit coupling. As an example of our approach, we reveal that triangular and honeycomb nano-hole arrays punctured in graphene yield topologically distinct states, and that in the patchwork of them topological interface states appear which are protected by an energy gap up to 0.5 eV . The unidirectional propagating interface states are dominated by a pseudospin, an emergent degree of freedom intimately related to the orbital angular momentum of the Bloch wavefunctions, which can be exploited for orbitronics functionality. Using nano holes with unbalanced numbers of carbon atoms in the two sublattices of honeycomb lattice, one may obtain spinful topological states, which hopefully can be developed for spintronics applications.
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