Here, the quantization of Dirac fermions in lithographically defined graphene nanoconstrictions is studied. Quantized conductance is observed in single nanoconstrictions fabricated on top of a thin hexamethyldisilazane layer over a Si/SiO2 wafer. This nanofabrication method allows to obtain well defined edges in the nanoconstrictions, thus reducing the effects of edge roughness on the conductance. The occurrence of ballistic transport is proved and several size quantization plateaus are identified in the conductance at low temperature. Experimental data and numerical simulations show good agreement, demonstrating that the smoothening of the plateaus is not related to edge roughness but to quantum interference effects.

We report here our recent electron transport results in spatially separated two-dimensional electron and hole gases with nominally degenerate energy subbands, realized in an InAs(10 nm)/GaSb(5 nm) coupled quantum well. We observe a narrow and intense maximum (∼500 kΩ) in the four-terminal resistivity in the charge neutrality region, separating the electron-like and hole-like regimes, with a strong activated temperature dependence above T=7 K and perfect stability against quantizing magnetic fields. We discuss several mechanisms for that unexpectedly large resistance in this zero-gap semi-metal system including the formation of an excitonic insulator state.

In this work, we find the exact transmission coefficient across one and two potential barriers in graphene. We obtain theoretical expressions for this coefficient in terms of the characteristics of the potential barriers, height, width and separation and the characteristics of the carriers, Fermi energy and incidence angle. This coefficient is essential in order to characterize the conductance in several electronic devices based on graphene. Since the calculated transmission coefficient is highly non-isotropic, we extend the Landauer formalism and obtain a closed expression for transistor conductance.

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