We calculate the Fermi energy dependence of the (time-averaged) current and shot noise in an impurity-free carbon bilayer (length L ≪ width W ), and compare with known results for a monolayer. At the Dirac point of charge neutrality, the bilayer transmits as two independent monolayers in parallel: Both current and noise are resonant at twice the monolayer value, so that their ratio (the Fano factor) has the same 1/3 value as in a monolayer -and the same value as in a diffusive metal. The range of Fermi energies around the Dirac point within which this pseudo-diffusive result holds is smaller, however, in a bilayer than in a monolayer (by a factor l ⊥ /L, with l ⊥ the interlayer coupling length).

We calculate the conductance G of a bipolar junction in a graphene nanoribbon, in the highmagnetic field regime where the Hall conductance in the p-doped and n-doped regions is 2e 2 /h. In the absence of intervalley scattering, the result G = (e 2 /h)(1 − cos Φ) depends only on the angle Φ between the valley isospins (= Bloch vectors representing the spinor of the valley polarization) at the two opposite edges. This plateau in the conductance versus Fermi energy is insensitive to electrostatic disorder, while it is destabilized by the dispersionless edge state which may exist at a zigzag boundary. A strain-induced vector potential shifts the conductance plateau up or down by rotating the valley isospin.

When smooth, zero-on-average, periodic magnetic and electric fields are applied to a carbon mono-layer (graphene), a gap between the valence and conduction band is introduced. Here this gapped state is studied analytically. It is found that it does not correspond to a band insulator: a constant electric field induces a quantized Hall current even though the magnetic flux through the sample is zero and there are no Landau levels. The phenomenon is of the same type as that discovered by Haldane for a graphene sample in a periodic magnetic field that is not smooth, i.e. varies rapidly on the scale of the graphene lattice constant. The effect can be explained in terms of the topological theory of Thouless, Kohmoto, Nightingale and den Nijs. For the system studied in this paper, an explanation in terms of simple physical principles is also presented. Thus some of the mystery is taken out of the apparently strange phenomenon of a Hall effect without magnetic flux. Furthermore, Haldane's model requires control over external magnetic fields on length scales less than an angstrom and is therefore hard to realize experimentally. For the model studied here, control over external fields on length scales that are larger by two orders of magnitude or more is sufficient. The model is therefore more amenable to experimental realization.

We present a derivation of the Keldysh action of a general multichannel time-dependent scatterer in the context of the Landauer-Büttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green's functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering full counting statistics and the Fermi-edge singularity.