Ballistic transport in graphene nanostructures

This work aims to contribute to the progress and understanding of the sources of disorder in nano-structured graphene devices. The first part of the thesis starts with the introduction of disordered two-terminal graphene nanoribbons of different aspect ratio, in order to unveil and characterize the amount of potential fluctuations on silicon dioxide ($SiO_2$) substrates. The experimental results reveal the diffusive nature of the transport behavior and a Coulomb blockade dominated transport regime close to the charge neutrality point. Besides its disordered nature, results appoint very short graphene constrictions, with levels of conductance close to $\sim \!0.1\,e^2/h$, as prime candidates for exploring Fano resonances in graphene nano-structures. In an attempt to reduce the contributions of the potential fluctuations to transport, we initially identify the different sources of disorder, with bulk and edges arising as the major contributors in nano-structured devices. The strong influence from the bulk is characterized via the tunneling processes through magnetically confined quantum dots arising from the aforementioned bulk disorder. First evidences of an edge induced disorder are treated in the following section, where we investigate the crystal structure of the nanoribbon's edges by means of Raman spectroscopy experiments. Results on lithography-free graphene nanoribbons, shaped by the exfoliation process itself, are compared to traditional plasma etched graphene ribbons. In these pristine ribbons, the correlation length $\xi$, figure of merit to characterize the edges, is one order of magnitude higher than on plasma etched structures. Results highlight the strong edge-induced disorder present in traditionally plasma-etched graphene devices. With the edge-induced disorder identified via Raman spectroscopy measurements, we implement in the next section an electrostatic approach to reduce its effects. Short and relatively narrow graphene constrictions are side-gated by graphene gate electrodes. We demonstrate the reduction in disorder by transport and bias spectroscopy measurements. Results are further supported by the formation of a quasi-1D channel upon application of a lateral electrostatic potential. The 1D-like nature of the electronic path is justified by its Fano-like interference with a 0D-like charged puddle located at the interface with the leads. Results represent the very first reported indications of Fano interference phenomena in graphene. To reduce bulk disorder, we implement a dry transfer technique for the fabrication of encapsulated graphene devices in between a top- and a bottom-layer of hexagonal boron nitride (hBN). Mobility values approaching $200\,000\,cm^2/(V\,s)$ confirm the high quality achieved with our fabrication technique. The residual disorder is characterized via the temperature dependence of the symmetry broken states in the quantum Hall regime, in a hBN/graphene/hBN Hall bar device. The values of localization length found in the variable-range-hopping (VRH) regime exceed $1\mu m$, one order of magnitude higher than the reported values for graphene on $SiO_2$ substrates. In the second part of the thesis, we demonstrate ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically-defined graphene quantum point contacts (QPCs). Close to the charge neutrality point, bias voltage spectroscopy measurements reveal a renormalized Fermi velocity ($v_F\!\approx\!1.5\times10^6\,m/s$) in our graphene constrictions. Moreover, at low carrier densities, transport measurements allow probing the density of localized states at the edges, thus offering a unique handle on edge physics in graphene devices. Direct comparison between successive cool-downs of a same QPC device reveal the lifting of the four-fold degenerate subbands. Results are supported by bias voltage and magnetic field dependent measurements. The amount of dopands/contaminants collected by the edges during the successive cool-downs is appointed as the source of this degeneracy breaking process. Quantum Hall measurements are used to spatially resolve the change in capacitance profile, supporting this change in dopands/contaminants at the edges