Hybrid lateral superlattices composed of a square array of antidots and a periodic one-dimensional magnetic modulation are prepared in $mathrm{Ga[Al]As}$ heterostructures. The two-dimensional electron gases exposed to these superlattices are characte
rized by magnetotransport experiments in vanishing average perpendicular magnetic fields. Despite the absence of closed orbits, the diagonal magnetoresistivity in the direction perpendicular to the magnetic modulation shows pronounced classical resonances. They are located at magnetic fields where snake trajectories exist which are quasi-commensurate with the antidot lattice. The diagonal magnetoresistivity in the direction of the magnetic modulation increases sharply above a threshold magnetic field and shows no fine structure. The experimental results are interpreted with the help of numerical simulations based on the semiclassical Kubo model.
The magnetoconductance of graphene nanoribbons with rough zigzag and armchair edges is studied by numerical simulations. nanoribbons with sufficiently small bulk disorder show a pronounced magnetoconductance minimum at cyclotron radii close to the ri
bbon width, in close analogy to the wire peak observed in conventional semiconductor quantum wires. In zigzag nanoribbons, this feature becomes visible only above a threshold amplitude of the edge roughness, as a consequence of the reduced current density close to the edges.
The transport through a quantum wire exposed to two magnetic spikes in series is modeled. We demonstrate that quantum dots can be formed this way which couple to the leads via magnetic barriers. Conceptually, all quantum dot states are accessible by
transport experiments. The simulations show Breit-Wigner resonances in the closed regime, while Fano resonances appear as soon as one open transmission channel is present. The system allows to tune the dots confinement potential from sub-parabolic to superparabolic by experimentally accessible parameters.
We derive analytical expressions for the conductivity of bilayer graphene (BLG) using the Boltzmann approach within the the Born approximation for a model of Gaussian disorders describing both short- and long-range impurity scattering. The range of v
alidity of the Born approximation is established by comparing the analytical results to exact tight-binding numerical calculations. A comparison of the obtained density dependencies of the conductivity with experimental data shows that the BLG samples investigated experimentally so far are in the quantum scattering regime where the Fermi wavelength exceeds the effective impurity range. In this regime both short- and long-range scattering lead to the same linear density dependence of the conductivity. Our calculations imply that bilayer and single layer graphene have the same scattering mechanisms. We also provide an upper limit for the effective, density dependent spatial extension of the scatterers present in the experiments.
The effects of Coulomb interactions on the electronic properties of bilayer graphene nanoribbons (BGNs) covered by a gate electrode are studied theoretically. The electron density distribution and the potential profile are calculated self-consistentl
y within the Hartree approximation. A comparison to their single-particle counterparts reveals the effects of interactions and screening. Due to the finite width of the nanoribbon in combination with electronic repulsion, the gate-induced electrons tend to accumulate along the BGN edges where the potential assumes a sharp triangular shape. This has a profound effect on the energy gap between electron and hole bands, which depends nonmonotonously on the gate voltage and collapses at intermediate electric fields. We interpret this behavior in terms of interaction-induced warping of the energy dispersion.
A theoretical study of the magnetoelectronic properties of zigzag and armchair bilayer graphene nanoribbons (BGNs) is presented. Using the recursive Greens function method, we study the band structure of BGNs in uniform perpendicular magnetic fields
and discuss the zero-temperature conductance for the corresponding clean systems. The conductance quantized as 2(n+1)G_ for the zigzag edges and nG_0 for the armchair edges with G_{0}=2e^2/h being the conductance unit and $n$ an integer. Special attention is paid to the effects of edge disorder. As in the case of monolayer graphene nanoribbons (GNR), a small degree of edge disorder is already sufficient to induce a transport gap around the neutrality point. We further perform comparative studies of the transport gap E_g and the localization length in bilayer and monolayer nanoribbons. While for the GNRs E_{g}^{GNR}is proportional to 1/W, the corresponding transport gap E_{g}^{BGN} for the bilayer ribbons shows a more rapid decrease as the ribbon width W is increased. We also demonstrate that the evolution of localization lengths with the Fermi energy shows two distinct regimes. Inside the transport gap, xi is essentially independent on energy and the states in the BGNs are significantly less localized than those in the corresponding GNRs. Outside the transport gap xi grows rapidly as the Fermi energy increases and becomes very similar for BGNs and GNRs.
A theoretical study of the transport properties of zigzag and armchair graphene nanoribbons with a magnetic barrier on top is presented. The magnetic barrier modifies the energy spectrum of the nanoribbons locally, which results in an energy shift of
the conductance steps towards higher energies. The magnetic barrier also induces Fabry-Perot type oscillations, provided the edges of the barrier are sufficiently sharp. The lowest propagating state present in zigzag and metallic armchair nanoribbons prevent confinement of the charge carriers by the magnetic barrier. Disordered edges in nanoribbons tend to localize the lowest propagating state, which get delocalized in the magnetic barrier region. Thus, in sharp contrast to the case of two-dimensional graphene, the charge carriers in graphene nanoribbons cannot be confined by magnetic barriers. We also present a novel method based on the Greens function technique for the calculation of the magnetosubband structure, Bloch states and magnetoconductance of the graphene nanoribbons in a perpendicular magnetic field. Utilization of this method greatly facilitates the conductance calculations, because, in contrast to excising methods, the present method does not require self-consistent calculations for the surface Greens function.
A poly(styrene-block-methylmethacrylate) diblock copolymer in the hexagonal cylindrical phase has been used as a mask for preparing a periodic gate on top of a Ga[Al]As-heterostructure. A superlattice period of 43 nm could be imposed onto the two-dim
ensional electron gas. Transport measurements show a characteristic positive magnetoresistance around zero magnetic field which we interpret as a signature of electron motion guided by the superlattice potential.
The magnetotransport properties of antidot lattices containing artificially designed grain boundaries have been measured. We find that the grain boundaries broaden the commensurability resonances and displace them anisotropically. These phenomena are
unexpectedly weak but differ characteristically from isotropic, Gaussian disorder in the antidot positions. The observations are interpreted in terms of semiclassical trajectories which tend to localize along the grain boundaries within certain magnetic field intervals. Furthermore, our results indicate how the transport through superlattices generated by self-organizing templates may get influenced by grain boundaries.
The electronic transport in polypyrrole thin films synthesized chemically from the vapor phase is studied as a function of temperature as well as of electric and magnetic fields. We find distinct differences in comparison to the behavior of both poly
pyrrole films prepared by electrochemical growth as well as of the bulk films obtained from conventional chemical synthesis. For small electric fields F, a transition from Efros-Shklovskii variable range hopping to Arrhenius activated transport is observed at 30 K. High electric fields induce short range hopping. The characteristic hopping distance is found to be proportional to F^(-1/2). The magnetoresistance R(B) is independent of F below a critical magnetic field, above which F counteracts the magnetic field induced localization.
