We have studied the resistance of a large number of highly oriented graphite samples with areas ranging from several mm 2 to a few µm 2 and thickness from ∼10 nm to several tens of micrometers. The measured resistance can be explained by the parallel contribution of semiconducting graphene layers with low carrier density < 10 9 cm −2 and the one from metallic-like internal interfaces. The results indicate that ideal graphite with Bernal stacking structure is a semiconductor with a narrow band gap E g ∼ 40 meV. Contents

Low-field magnetotransport measurements of topological insulators such as Bi2Se3 are important for revealing the nature of topological surface states by quantum corrections to the conductivity, such as weak-antilocalization. Recently, a rich variety of high-field magnetotransport properties in the regime of high electron densities (∼1019 cm−3) were reported, which can be related to additional two-dimensional layered conductivity, hampering the identification of the topological surface states. Here, we report that quantum corrections to the electronic conduction are dominated by the surface states for a semiconducting case, which can be analyzed by the Hikami-Larkin-Nagaoka model for two coupled surfaces in the case of strong spin-orbit interaction. However, in the metallic-like case this analysis fails and additional two-dimensional contributions need to be accounted for. Shubnikov-de Haas oscillations and quantized Hall resistance prove as strong indications for the two-dimensional layered metallic behavior. Temperature-dependent magnetotransport properties of high-quality Bi2Se3 single crystalline exfoliated macro and micro flakes are combined with high resolution transmission electron microscopy and energy-dispersive x-ray spectroscopy, confirming the structure and stoichiometry. Angle-resolved photoemission spectroscopy proves a single-Dirac-cone surface state and a well-defined bulk band gap in topological insulating state. Spatially resolved core-level photoelectron microscopy demonstrates the surface stability.

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The intrinsic values of the carriers mobility and density of the graphene layers inside graphite, the well known structure built on these layers in the Bernal stacking configuration, are not well known mainly because most of the research was done in rather bulk samples where lattice defects hide their intrinsic values. By measuring the electrical resistance through microfabricated constrictions in micrometer small graphite flakes of a few tens of nanometers thickness we studied the ballistic behavior of the carriers. We found that the carriers' mean free path is micrometer large with a mobility µ ≃ 6 × 10 6 cm 2 /Vs and a carrier density n ≃ 7 × 10 8 cm −2 per graphene layer at room temperature. These distinctive transport and ballistic properties have important implications for understanding the values obtained in single graphene and in graphite as well as for implementing this last in nanoelectronic devices.

Using a linear array of voltage electrodes with a separation of several micrometers on a 20 nm thick and 30 µm long multigraphene sample we show that the measured resistance does not follow the usual length dependence according to Ohm's law. The deviations can be quantitatively explained taking into account Sharvin-Knudsen formula for ballistic transport. This allows us to obtain without free parameters the mean free path of the carriers in the sample at different temperatures. In agreement with recently reported values obtained with a different experimental method, we obtain that the carrier mean free path is of the order of ∼ 2 µm with a mobility µ ∼ 10 7 cm 2 V −1 s −1 . The results indicate that the usual Ohm's law is not adequate to calculate the absolute resistivity of mesoscopic graphite samples.