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We have performed magnetotransport measurements on a multi-layer graphene flake. At the crossing magnetic field Bc, an approximately temperature-independent point in the measured longitudinal resistivity, which is ascribed to the direct insulator-quantum Hall (I-QH) transition, is observed. By analyzing the amplitudes of the magnetoresistivity oscillations, we are able to measure the quantum mobility of our device. It is found that at the direct I-QH transition, the product of the quantum mobility and is about 0.37 which is considerably smaller than 1. In contrast, at Bc, the longitudinal resistivity is close to the Hall resistivity, i.e., the product of the classical mobility and the crossing field is about 1. Therefore our results suggest that different mobilities need to be introduced for the direct I-QH transition observed in multi-layered graphene. Combined with existing experimental results obtained in various material systems, our data obtained on graphene suggest that the direct I-QH transition is a universal effect in 2D.
We have performed low-temperature transport measurements on a disordered two-dimensional electron system (2DES). Features of the strong localization leading to the quantum Hall effect are observed after the 2DES undergoes a direct insulator-quantum H
Using the random matrix theory, we investigate the ensemble statistics of edge transport of a quantum spin Hall insulator with multiple edge states in the presence of quenched disorder. Dorokhov-Mello-Pereyra-Kumar equation applicable for such a syst
Magneto-transport measurements are performed on the two-dimensional electron system (2DES) in an AlGaAs/GaAs heterostructure. By increasing the magnetic field perpendicular to the 2DES, magnetoresistivity oscillations due to Landau quantisation can b
Reports of metallic behavior in two-dimensional (2D) systems such as high mobility metal-oxide field effect transistors, insulating oxide interfaces, graphene, and MoS2 have challenged the well-known prediction of Abrahams, et al. that all 2D systems
Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $eta$ characterizing the decay of wave functi