Strain-induced one-dimensional Landau level quantization in corrugated graphene

Theoretical research has predicted that a ripple of graphene generates an effective gauge field on its low-energy electronic structure and could lead to Landau quantization. Here, we demonstrate using a combination of an experimental method (scanning tunneling microscopy) and a theoretical approach (tight-binding approximation) that Landau levels will form when the effective pseudomagnetic flux per ripple Φ~(h²/la)Φ₀ is larger than the flux quantum Φ₀ (here, h is the height, l is the width of the ripple, and a is the nearest C-C bond length). The strain-induced gauge field in the ripple only results in one-dimensional (1D) Landau-level quantization along the ripple. Such 1D Landau quantization does not exist in two-dimensional systems in an external magnetic field. Its existence offers a unique opportunity to realize interesting electronic properties in strained graphene.