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We carry out a comprehensive computational study on the stability of the Dirac cone in artificial graphene realized in nanopatterned quantum wells. Our real-space approach allows us to vary the size, shape, and positioning of the quantum dots in the hexagonal lattice. We compare the (noninteracting) single-particle calculations to density-functional studies within both local-density approximation and meta-generalized-gradient approximation. Furthermore, the density-functional results aredoi:10.1088/1367-2630/18/8/083014 fatcat:z6zhl2ihpndpvfunbenuuemjrq