Charge and spin transport in graphene
Graphene is a monolayer of carbon atoms arranged into a two dimensional honeycomb lattice. Due to its exceptional band structure, charge carriers in graphene exhibit exciting physical properties which result in unconventional (magneto-)transport phenomena such as the room temperature quantum hall effect bagging the Nobel prize in 2010. Moreover, graphene is a promising material for spintronic applications  due to its high carrier mobility at room temperature and its long spin life time. We investigate the spin injection and the spin transport in graphene by using a nonlocal spin valve geometry [1, 2] with ferromagnetic electrodes as spin injector and detector. In addition to conventional sources for spin-polarized current such as ferromagnetic metals we also investigate ferromagnetic tunnel barriers which create two different barrier heights for spin-up and spin-down electrons .
In graphene which is doped by heteroatom substitution some of the carbon atoms are replaced by different atoms such as nitrogen or boron (as shown in Fig. 2). With Chemical Vapor Deposition (CVD) this can be achieved during the growth process and by changing the growth-parameters the level of doping can be varied. Doping leads to clear changes in the properties as for example an increase in charge carrier density and the possibility of opening a bandgap .
Figure 2: Schematic illustration of the lattice of doped graphene with the carbon atoms depicted as black nodes and the respective dopant in red, green or yellow.
Furthermore, the change in resistance when applying a magnetic field – the magnetoresistance – changes its field-dependence and even the sign.
Geometrically confining graphene into narrow ribbons (Graphene Nanoribbons - GNRs) will give rise to new phenomena unknown in extended graphene flakes and films. They occur because the edges in a system of finite size break translational invariance and thus, break also the equivalence of the two triangular Bravais lattices that build the hexagons. Hence, GNRs have been theoretically predicted to exhibit a band gap that can be tuned by tailoring their width and edge geometry (zigzag/armchair, Fig. 4) . However, this tuning demands a well-controlled production process with plenty of opportunities for novel geometries. Furthermore, pure graphene spin valves without the need of the ferromagnetic electrodes are predicted since intrinsic edge magnetism is expected for well-defined graphene nanostructures. 
Figure 4: Armchair- and zigzag-edges in graphene. a1 and a2 denote the basic vectors of the triangular Bravais lattice. dnn = 0.142 nm is the lattice constant.
Besides single layer graphene, few- and multilayer systems exhibit also exciting properties. In turbostratic graphene stacks the layers are rotated with respect to each other leading to an electronic decoupling. It is thus a promising candidate to combine the electronic properties of single layer graphene with the robustness of graphitic microstructures. The common way to produce high quality turbostratic graphene is the epitaxial growth on the C-face of silicon carbide . Alternatively, a plasma arc process yields discs comprised of 60 - 150 graphene layers. They typically exhibit large charge carrier mobilites of 105 cm2/Vs and show 2D transport features, such as weak localization , demonstrating the effective decoupling of adjacent graphene layers.