Dirac Point and Edge States in a Microwave Realization of Tight-Binding Graphene-like Structures

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We present a microwave realization of finite tight-binding graphene-like structures. The structures are realized using discs with a high index of refraction. The discs are placed on a metallic surface while a second surface is adjusted atop the discs, such that the waves coupling the discs in the air are evanescent, leading to the tight-binding behavior. In reflection measurements the Dirac point and a linear increase close to the Dirac point is observed, if the measurement is performed inside the sample. Resonances due to edge states are found close to the Dirac point if the measurements are performed at the zigzag-edge or at the corner in case of a broken benzene ring.