The atomic and electronic structures of Au-intercalated graphene buffer layer on SiC(0001) surface were investigated using first-principles calculations. The unique Dirac cone of the graphene near K point reappeared as the buffer layer was intercalated by Au atoms. Coherence interfaces were used to study the mismatch and strain at the interfaces. Our calculations showed that the strain at graphene/Au and Au/SiC(0001) interfaces also played a key role in the electronic structures. Futhermore, we found that at Au coverage of 3/8 ML, Au intercalation leads to strong n-type doping of graphene. At 9/8 ML, it exhibited weak p-type doping, meaning that graphene is not fully decoupled from substrate. The shift of Dirac point resulting from electronic doping is not only due to different electronegativities but also strains at the interfaces. Our calculated positions of Dirac points are consistent with those observed in the ARPES experiment [Isabella Gierz et al., Phys. Rev. B 81, 235408 (2010).].

Field-effect transistors (FET) based on graphene as channel has extraordinaryproperties in terms of charge mobility, charge carrier density etc. However, there aremany challenges to graphene based FET due to the fact graphene is a monolayer ofatoms in 2-dimentional space that is strongly influenced by the operating conditions.One issue is that the Dirac point, or K-point, shifts to higher gate voltage whengraphene is exposed to atmosphere. In this study graphene field-effect transistors(GFET) based on commercially available CVD graphene are electrically characterizedthrough field effect gated measurements. The Dirac point is initially unobservable andlocated at higher gate voltages (>+42 V), indicating high p-doping in graphene.Different treatments are tried to enhance the properties of GFET devices, such astransconductance, mobility and a decrease of the Dirac point to lower voltages, thatincludes current annealing, vacuum annealing, hot plate annealing, ionized water bathand UV-ozone cleaning. Vacuum annealing and annealing on a hot plate affect thegated response; they might have decreased the overall p-doping, but also introducedDirac points and non-linear features. These are thought to be explained by localp-doping of the graphene under the electrodes. Thus the Dirac point of CVDgraphene is still at higher gate voltages. Finally, the charge carrier mobility decreasedin all treatments except current – and hot plate annealing, and it is also observed that charge carrier mobilities after fabrication are lower than the manufacturer estimatesfor raw graphene on SiO2/Si substrate.

This thesis describes studies on two-dimensional electron gases (2DEG) in graphene and related 2D systems. Magnetotransport investigations specifically in graphene and its bilayer system are demonstrated in detail, while the experimental techniques presented in this thesis are widely applicable to a large variety of other 2D materials. Chapter 1 gives an introduction and motivation for the principal topic presented in this thesis, with a general introduction to carbon nano-materials and an overview of the current state of graphene-related research and technological development (RTD). Chapter 2 establishes a basic theoretical framework which is essential for interpreting the results presented in this thesis, starting with the crystal and electronic band structures of graphene and its bilayer, followed by high magnetic fields effects on transport properties in these 2D systems. Chapter 3 details the experimental methods directly related to the presented work. The next three chapters report experimental results of three specific magnetotransport studies. Chapter 4 reports the disorder effects on epitaxial graphene in the vicinity of the Dirac point. Quadratic increases of carrier densities with temperature are found to be due to intrinsic thermal excitation combined with electron-hole puddles induced by charged impurities. It is also shown that the minimum conductivity increases with increasing disorder strength, in good agreement with quantum-mechanical numerical calculations. Chapter 5 reports measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to a magnetic field dependent charge transfer process from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels this process is modelled in excellent agreement with experimental results. In Chapter 6, energy relaxation of hot carriers in graphene bilayer systems is investigated from measurements on Shubnikovde Haas oscillations and weak localisation. The hot-electron energy loss rate follows the predicted T⁴ power-law at carrier temperatures from 1.4 up to about 100 K, due to electron-acoustic phonon interactions. Comparisons are made between graphene monolayer and bilayer systems and a much stronger carrier density dependence of the energy loss rate is found in the bilayer system. This thesis concludes with a summary of the most important findings of the topics that have been discussed. The significance and limitations of the present research are listed. Some suggestions and outlook are given for possible improvements and interesting areas of future research and development.

This diploma thesis deals with electrical conductivity of a graphene sample, preparation of a graphene field-effect transistor and his irradiation by electron beam. In the theoretical part of the thesis, we describe electronic properties of graphene, preparation of graphene by CVD and its transfer to Si substrate with SiO_2 layer. Experimental part of this thesis is focused on the preparation of a graphene field-effect transistor for use in UHV conditions. Futher describes electron beam scanning over the transistor and creation of current maps of tranzistor. In the last part, the thesis deals with influence of electron beam on transport properties of graphene layer and doping of graphene layer by electron beam.

This master's thesis deals with the study of electric properties of graphene layers covered by Ga atoms in UHV conditions. The substrates were prepared by using laser litography and the graphene layer was prepared by using chemical vapor deposition (CVD). Dependence of Dirac point location on gallium atoms deposition time and influence of electrical properties of graphene on hydrogen atoms deposition time were studied. Experimental results and their evaluation are discussed.

Les cristaux granulaires sont des structures périodiques de particules disposées en réseau cristallin. Les interactions entre ces billes peuvent être modélisées par leurs contacts, qui ont des dimensions et des masses effectives beaucoup plus petites que celles des billes. Ceci induit une propagation d'ondes élastiques dans les structures granulaires avec des vitesses significativement plus lentes que dans le matériau des grains individuels. En outre, en raison de forces de cisaillement non centrales, les rotations de particules peuvent être initiées, conduisant à des modes de phononiques supplémentaires dans ces cristaux. Dans ce manuscrit, on étudie la propagation d’ondes dans les cristaux granulaires monocouche bidimensionnels avec un mouvement des particules hors-plan ou dans le plan. Les propriétés phononiques sont étudiées, y compris les points de Dirac, les modes de fréquence nulle, les modes à vitesse de groupe nulle et leur transformation en modes de propagation lente. En outre, en présence de bords, on peut prévoir également des ondes de bord élastiques à fréquence nulle et extrêmement lentes dans des cristaux granulaires en « nid d'abeille » (graphène granulaire). En outre, les propriétés topologiques des ondes de bord rotationelles-transverses dans un graphène granulaire sont théoriquement démontrées. En induisant une transition topologique, qui transforme l'ordre topologique du graphène granulaire de trivial en non trivial, on peut observer le transport de bord topologique dans le graphène granulaire. Les théories développées pourraient mener potentiellement à des applications sur le contrôle des ondes élastiques par des structures granulaires. / Granular crystals are spatially periodic structures of elastic particles arranged in crystal lattices. The interactions between particles take place via their elastic interconnections, which are of much smaller dimensions and weights than the beads. This induces propagation of elastic waves in granular structures at significantly slower velocities than in the individual grains. In addition, due to the existence of non-central shear forces, rotations of particles can be initiated, leading to extra phononic modes in the crystals. In the manuscript, wave dynamics in two-dimensional monolayer granular crystals with either out-of-plane or in-plane particle motion is studied. The phononic properties are investigated, including Dirac points, zero-frequency modes, zero-group-velocity modes and their transformation into slow propagating phononic modes. Furthermore, in the presence of edges/boundaries, zero-frequency and extremely slow elastic edge waves can be also predicted in mechanical granular honeycomb crystals (granular graphene). In addition, topological properties of rotational edge waves in a granular graphene are theoretically demonstrated. By inducing topological transition, which turns the topological order of granular graphene from trivial to nontrivial, topological edge transport in the granular graphene can be observed. The developed theories could promote the potential applications of designed granular structures with novel elastic wave propagation properties.