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We have achieved mobilities in excess of 200,000 cm^2/Vs at electron densities of ~2*10^11 cm^-2 by suspending single layer graphene. Suspension ~150 nm above a Si/SiO_2 gate electrode and electrical contacts to the graphene was achieved by a combination of electron beam lithography and etching. The specimens were cleaned in situ by employing current-induced heating, directly resulting in a significant improvement of electrical transport. Concomitant with large mobility enhancement, the widths of the characteristic Dirac peaks are reduced by a factor of 10 compared to traditional, non-suspended devices. This advance should allow for accessing the intrinsic transport properties of graphene., 4 pages, 3 figures, references updated

The quantum Hall (QH) effect in two-dimensional electron and hole gas is studied in high quality graphene samples. Graphene samples whose lateral size ∼10 μm were fabricated into mesoscopic devices for electrical transport measurement in magnetic fields. In an intermediate field range of up to 10 T, a distinctive half-integer QH effect is discovered with QH plateaus appearing at a filling factor sequence, ν = 4 ( n + 1 / 2 ) , where n is the Landau level (LL) index. As the magnetic field increases to the extreme quantum limit, we observe additional QH plateaus at filling factors ν = 0 , ± 1 , ± 4 . Further detailed investigations show that the presence of the ν = 0 , ± 1 QH states indicates the n = 0 LL at the charge neutral Dirac point splits into four sublevels. This lifts both the sublattice and the spin degeneracy, while the QH states at ν = ± 4 can be attributed to lifting of the spin degeneracy of the LLs. Above 30 T of magnetic field, the large quasiparticle gaps between the n = 0 and n = ± 1 LLs lead to the QH effect that can be observed even at room temperature.

In this paper, we review low temperature electronic transport results in high quality two-dimensional electron systems. We discuss the quantization of the diagonal resistance, R x x , at the edges of several quantum Hall states. Each quantized R x x value turns out to be close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R x y . Moreover, peaks in R x x occur at different positions in positive and negative magnetic fields. All three R x x features can be explained quantitatively by a ∼1% cm electron density gradient. Furthermore, based on this observation, the well known but still enigmatic resistivity rule, relating R x x to d R x y / d B , finds a simple interpretation in terms of this gradient. In another sample, at 1.2 K, R x x we observe a strongly linear magnetic field dependence. Surprisingly, this linear magnetoresistance also originates from the density gradient. Our findings throw an unexpected light on the relationship between the experimentally measured R x x and the diagonal resistivity ρ x x .

A short review of recent developments in the area of the fractional quantum Hall effect is presented. The article attempts to develop some intuitive images of the highly-correlated electron behavior. It emphasizes the new states at half-filled landau levels and their composite fermion quasiparticles. Recent theoretical calculations promise yet more bizarre electronic states to be discovered by experiment.