Strain Induced One-Dimensional Landau-Level Quantization in Corrugated Graphene

Theoretical research has predicted that ripples of graphene generates effective gauge field on its low energy electronic structure and could lead to zero-energy flat bands, which are the analog of Landau levels in real magnetic fields. Here we demonstrate, using a combination of scanning tunneling microscopy and tight-binding approximation, that the zero-energy Landau levels with vanishing Fermi velocities will form when the effective pseudomagnetic flux per ripple is larger than the flux quantum. Our analysis indicates that the effective gauge field of the ripples results in zero-energy flat bands in one direction but not in another. The Fermi velocities in the perpendicular direction of the ripples are not renormalized at all. The condition to generate the ripples is also discussed according to classical thin-film elasticity theory.