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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. [ABSTRACT FROM AUTHOR]

Using cryogenic scanning tunneling microscopy and scanning tunneling spectroscopy+ single-electron tunneling of Au nanoparticles (NPs) with 1.4 nm in radius was studied. We observe a gap ΔV ~ 2e/C (C is the capacitance of the Au particle and e the charge of an electron) around zero bias in the tunneling-conductancc spectrum, followed by a series of discrete single-electron tunneling peaks with peak spacing of EC ~ e/C at both negative and positive bias. Experimental data are well explained by taking into account both the shift o1 conductance peaks and the effect of exchange interaction of electrons on the single-electron tunneling of Au NPs. A conductance peak near zero bias was suppressed by the exchange-type zero-bias anomaly, which results in the gap Δ V ~ 2EC. According to our experiment and analysis, the shift of conductance peaks of Au NPs is attributed to self-biased gate and/or tip-induced gate. [ABSTRACT FROM AUTHOR]