An epitaxial layer of graphene was grown on a pre patterned 6H-SiC(0001) crystal. The graphene smoothly covers the hexagonal nano-holes in the substrate without the introduction of small angle grain boundaries or dislocations. This is achieved by an elastic deformation of the graphene by ≈0.3% in accordance to its large elastic strain limit. This elastic stretching of the graphene leads to a modification of the band structure and to a local lowering of the electron group velocity of the graphene. We propose to use this effect to focus two-dimensional electrons in analogy to simple optical lenses.

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