Local measurements of tunneling magneto-conductance oscillations in monolayer, Bernal-stacked bilayer, and ABC-stacked trilayer graphene

Shubnikov-de Haas oscillations are the most well-known magneto-oscillations in transport measurements. They are caused by Landau quantization of two-dimensional(2D) electron systems in the presence of a magnetic field. Here we demonstrate that a scanning tunneling microscope(STM) can locally measure similar magneto-oscillations in 2D systems. In Landau level spectroscopy measurements with fine magnetic-field increments, we observed fixed-energy magnetic-field-dependent oscillations of the local density of states. From the measured tunneling magneto-conductance oscillations acquired by STM, energymomentum dispersions and Berry phases of a monolayer, Bernal-stacked bilayer, and ABC-stacked trilayer graphene were obtained. The reported method is applicable to a wide range of materials because it can obtain the magneto-oscillations of 2D systems larger than the magnetic length;importantly, it also requires no gate electrode.