Dielectrics have been an integral part of the electron devices and will likely resume playing a significant role in the future of nanoelectronics. An important step in assessing graphene potential as an alternative channel material for future electron devices is to benchmark its transport characteristics when integrated with dielectrics. Using back-gated and dual gated graphene field-effect transistors with top high-k metal-oxide dielectric, we study the dielectric thickness dependence of the carrier mobility. We show the carrier mobility decreases after deposition of metal-oxide dielectrics by atomic layer deposition (ALD) thanks to the Coulomb scattering by charged point defects in the dielectric. We investigate a novel method for the ALD of metal-oxide dielectrics on graphene, using an ultrathin nucleation layer that enables the realization of graphene field-effect transistors with aggressively scaled gate dielectric thickness. We show the nucleation layer significantly affects the quality of the subsequently deposited dielectric. In addition, we study transport characteristics of double layer systems. We demonstrate heterostructures consisting of two rotationally aligned bilayer graphene with an ultra-thin hexagonal boron nitride dielectric in between fabricated using advanced layer-by-layer transfer as well as layer pickup techniques. We show that double bilayer graphene devices possess negative differential resistance and resonant tunneling in their interlayer current-voltage characteristics in a wide range of temperatures. We show the resonant tunneling occurs either when the charge neutrality points of the two bilayer graphene are energetically aligned or when the lower conduction sub-band of one layer is aligned with the upper conduction sub-band of the opposite layer. Finally, we study the Raman spectra and the magneto-transport characteristics of A-B stacked and rotationally misaligned bilayer graphene deposited by chemical-vapor-deposition (CVD) on Cu. We show that the quantum Hall states (QHSs) sequence of the CVD grown A-B stacked bilayer graphene is consistent with that of natural bilayer graphene, while the sequence of the QHSs in the CVD grown rotationally misaligned bilayer graphene is a superposition of monolayer graphene QHSs. From the magnetotransport measurements in rotationally misaligned CVD-grown bilayer we determine the layer densities and the interlayer capacitance. / text

In this thesis, we use rst principles density functional theory (DFT) to study the energetics, structural and electronic properties of hydrogenated and lithiated bilayer graphene material systems. The newly developed four variants of the non-local van der Waals (vdW) exchange-correlation functionals (vdW-DF, vdW-DF2, vdW-DF C09x and vdW-DF2 C09x) are employed to explore all the possible con gurations of hydrogen adsorption at 50% and 100% coverage on a 1 1 unit cell. The results obtained are also compared with the GGA PBE functional. For 50% hydrogen coverage, 16 unique con gurations are identi ed in the unrelaxed state. Formation energy analysis reveals six possible energetically favourable con gurations with three low-energy competing con gurations. It is found that the properties of hydrogenated bilayer graphene greatly depend on the hydrogen con guration. For instance, the formation of a hydrogen dimer within the layers decouples the structure, whereas the dimer formation outside surfaces does not have a signi cant in uence on the van der Waals forces; thus the bilayers remain coupled. In this coupled con guration, the vdW-DF C09x functional predicts the lowest formation energy and shortest interlayer separation, whereas the GGA PBE functional gives the highest formation energy and largest interlayer distance. The reasons behind the variation of these functionals are discussed. Two of the three low-energy competing con gurations exhibit semimetallic behaviour, whereas the remaining con guration is a wide band gap material. The wide band gap structure is found to undergo a hydrogen-induced spontaneous phase transformation from hexagonal to tetrahedral (diamond-like) geometry. We conclude that this wide band gap con guration represents a viable template for synthesizing nanodiamonds from graphene by hydrogenation. At 100% coverage, ten unique hydrogen con gurations are identi ed from a 1 1 unit cell. All exchange-correlation functionals predict nine of the structures to have negative formation energies. From these nine structures, three low-energy competing structures are noted and found to be wide band gap semiconductors, whereas the other con gurations exhibit either a semimetallic or metallic character. Although a 1 1 unit-cell is able to present a clear picture for the interaction between hydrogen and graphene, our results reveal that it limits the occurrence of other interesting physics. The cell size was increased to 2 1, to identify other low-energy con gurations that are not possible in a 1 1 cell. The identi ed con gurations have shown physically interesting hydrogen arrangements such as chair-like, zigzag-like and boat-like con gurations. Furthermore, our results reveal that hydrogenation reduces the elastic properties of the pristine structures. We further perform a systematic investigation of the e ects of lithium (Li) on AA and AB stacking sequences of bilayer graphene. Two Li atoms are considered to examine the e ects of the Li-Li interaction on bilayer graphene, and a total of 12 unique con gurations for AB and 9 for AA stackings are identi ed. The vdW-DF consistently predicts the highest formation energies, whereas vdW-DF2 C09x gives the lowest. Unlike in the case of the pristine structures, it is noted that for lithiated bilayer graphene, GGA PBE gives comparable results to the other functionals. One of the Li intercalated con gurations undergoes a spontaneous translation from the AB to AA stacking, and is found to be the most energetically stable con guration. We therefore conclude that Li favours the AA stacking, and that con guration represents a feasible template for experimentally synthesizing and characterizing a Li-based anode material. We noticed that all identi ed Li con gurations exhibit metallic behaviour. Lastly, we found that the intercalated Li dimer weakly interacts with the graphene layers, whereas the intercalated isolated Li atom exhibits strong interaction. / Thesis (PhD)--University of Pretoria, 2014. / gm2014 / Physics / unrestricted

Thesis (M. Sc. (Physics)) -- University of Limpopo, 2016. / Bilayer graphene and single-walled carbon nanotubes were studied through classical molecular dynamics using Tersoff potential. The Tersoff potential has been the most successful model to replicate much of the semiconducting properties in carbon structures. The simulations were performed within a canonical (NVT) ensemble for structural properties and isothermal–isobaric ensemble (NPT) for thermodynamic properties of both materials. The bilayer graphene consists of two models of 64 and 256 atoms. Single-walled carbon nanotubes consist of three chiral structures of 264 atoms which is cnt(12,10), 260 atoms which is cnt(10,12) and armchair structure of 312 atoms which is cnt(12,12). The structural and thermodynamics properties were investigated in a range of temperature from 300 - 5000 K. It has been found that some of the properties of the graphene and carbon nanotube are similar. Graphene256 was found to be more stable than graphene64 and the armchair cnt(12,12) appears to be more mechanically stable than chiral cnt(12,10). Graphene and single-walled carbon nanotubes were also studied using X-ray diffraction and atomic force microscopy (AFM). The lattice constant for both materials were calculated and they agree well with the computational results. For carbon nanotubes, different solvents were used for characterization using the AFM. Chloroform was the best solvent since we managed to find some bundles of carbon nanotube. For ethanol and toluene solvents we did not managed to get any bundles. The diameter of single-walled carbon nanotube was determined only on a solution that chloroform solvent was used.

Résumé : Nous étudions dans cette thèse plusieurs propriétés du gaz d’électrons bidimensionnel (GE2D) dans le graphène et la bicouche de graphène (BG). Nous commençons par étudier la nature des excitations à une particule du GE2D dans le graphène près des facteurs de remplissage entiers dans les niveaux de Landau N [pas égal à] 0. Nous utilisons une approche de type Hartree-Fock (HF) pour comparer l’énergie de l’excitation d’une paire électron-trou à celle d’une paire skyrmion (SK)-antiskyrmion (ASK). Dans le graphène, les excitations SK et ASK sont des excitations chargées avec une texture de spin et/ou de pseudospin de vallée qui est quantifiée topologiquement. Nos calculs montrent que les paires SK-ASK sont les excitations chargées de plus basse énergie jusqu’au niveau de Landau |N| = 3. Notre approche permet en plus de calculer le domaine de couplage Zeeman pour lequel les paires SK-ASK sont les excitations de plus basse énergie et de déterminer comment l’énergie de ces paires est modifiée par les corrections d’écrantage. Le diagramme de phase du GE2D dans la bicouche de graphène a fait l’objet d’intenses recherches théoriques et expérimentales [8, 13, 15, 16], mais jusqu’à maintenant, seuls les états uniformes ont été considérés. Nous adaptons notre approche HF à l’étude des états non uniformes pour montrer que le GE2D dans la BG à remplissage ν = −1 dans le niveau de Landau N = 0 subit une série de transitions de phase lorsqu’un champ électrique perpendiculaire à la BG est appliqué. Nous étudions tout particulièrement les phases comportant une texture de pseudospin orbital soit un cristal de skyrmions et une phase spirale. Nous calculons les modes collectifs de ces phases ainsi que leur absorption électromagnétique. Nous poursuivons ensuite avec une étude des phases cristallines autour de certains remplissages entiers dans la BG. Le GE2D dans la bicouche de graphène a principalement été étudié dans le niveau de Landau N = 0. Comme dernier problème, nous étudions le diagramme de phase lorsqu’un nombre entier de niveaux de Landau est occupé dans les niveaux supérieurs |N| > 0. Alors que l’état fondamental du GE2D dans le graphène pour ces mêmes niveaux est un ferroaimant de Hall quantique (FHQ) avec une symétrie SU(2) pour le spin (en l’absence de couplage Zeeman) et le pseudospin de vallée, le GE2D dans la BG a plutôt un comportement FHQ de type Ising avec une symétrie Z[indice inférieur 2] à champ électrique nul. Cette différence de comportement a une grande influence sur la nature des transitions de phase possibles ainsi que sur celle des excitations topologiques. // Abstract : In this thesis, we study several properties of the two-dimensional electron gas (2DEG) in graphene and bilayer graphene. We first study the nature of the single-particle excitations in graphene near integer filling factors in Landau levels (LLs) N [not equal to] 0. We use a Hartree-Fock approach to compare the energy of an electron-hole excitation pair with that of a Skyrmion-antiskyrmion pair. In graphene, Skyrmions are charged excitations with a topological quantized spin and/or valley pseudo-spin texture. We give the range of Zeeman coupling for which Skyrmion-antiskyrmion has the lowest energy up to LL N = 3. Then we discuss how screening corrections modifies these results. The phase diagram of the 2DEG in bilayer graphene had been studied previously by a number of authors [8, 13, 15, 16] but only uniform states had been considered. Extending the Hartree-Fock approach to non-uniform states, we show that at filling factor ν = −1 in LL N = 0, the 2DEG goes through a series of phase transitions as the bias from an external electric field between two layers is increased. We study a crystal phase with orbital SK textures and a spiral state with the orbital pseudospin rotating in space. We compute the collective mode of these phases and their signatures in electromagnetic absorption experiments. We finally extend the Hartree-Fock approach to study the crystal states with valley or orbital textures near integer filling factors. The research on the 2DEG in bilayer graphene has been focussed almost exclusively in LL N = 0. As our last problem, we study the phase diagram at quarter and half fillings of the quartet of states in LLs |N| > 0. While the ground state of the 2DEG in graphene in |N| > 0 is a valley and spin quantum Hall ferromagnet with SU(2) symmetry in the absence of Zeeman coupling, the ground state in bilayer graphene is an Ising quantum Hall ferromagnet with a Z[subscript 2] valley symmetry at zero bias. We note that this change has important consequences on the nature of the transport properties and the single-particle excitations at integer fillings.

In the first part of this work, we describe a theory of the ground states and charge gaps in the fractional quantum Hall states of graphene. The theory relies on knowledge of these properties for filling fractions smaller than one. Then, by the application of two mapping rules, one is able to obtain these properties for fractional quantum Hall states at arbitrary fillings, by conceiving the quantum Hall ferromagnets as vacua on which correlated electrons or correlated holes are added. The predicted charge gaps and phase transitions between different fractional quantum Hall states are in good agreement with recent experiments. In the second part, we investigate the low energy theory for the neutral Landau level of bilayer graphene. We closely analyze the way different terms in the Hamiltonian transform under the action of particle-hole conjugation symmetries, and identify several terms that are relevant in explaining the lack of such symmetry in experiments. Combining an accurate parametrization of the electronic structure of bilayer graphene with a systematic account of the impact of screening we are able to explain the absence of particle-hole symmetry reported in recent experiments. We also study the energetics of fractional quantum Hall states with coherence between n=0 and n=1 cyclotron quantum numbers, and obtain a general formula to map the two-point correlation function from their well-known counterparts made from only n=0 quantum numbers. Bilayer graphene has the potential for realizing these states which have no analogue in other two-dimensional electron systems such as Gallium Arsenide. We apply this formula to describe the properties of the n=0/n=1 coherent Laughlin state which displays nematic correlations. / text

This thesis reports the discovery of a wide negative di↵erential resistance (NDR) region in a graphite-silicone composite that was utilized to create a strain-tuned flexible oscillator. Encoding the strain into frequency mimics the behavior of mechanoreceptor neurons in the skin and demonstrates a flexible and electronically active material suitable for state of the art bio-electronic applications. The NDR was investigated over a range of composite filling fractions and temperatures; alongside theoretical modelling to calculate the tunneling current through a graphite-silicone barrier. This led to the understanding that the NDR is the result of a semi-metal to insulator transition of embedded graphene bilayers within the graphite nanoparticles. The transition, brought about by a transverse bias across specifically orientated particles, opens a partial band-gap at the Fermi level of the bilayer. NDR in a flexible material has not been observed before and has potential for creating a flexible active device. The electromechanical properties of the composite were considered through a bend induced bilayer strain. The piezoresistance was found to be dominated by transient resistance spiking from the breaking of conduction lines, which then reform according to the viscoelasticity of the polymer matrix. The resistance spiking was embraced as a novel method for sensitive di↵erential pressure detection, used in the development of two applications. Firstly, it was employed for the detection of ultrasound waves and found to have an acoustic pressure detection threshold as low as 48 Pa. A commensurability was observed between the composite width and ultrasound wavelength which was shown to be consistent with the formation of standing waves, described by Bragg’s law. Secondly, a differential pressure array of 64 composite pixels was fabricated and demonstrated to image pressures under 3.8 kPa at a resolution of 10 dpi. The NDR active region was incorporated into an LC circuit where it was demonstrated to sustain oscillations of up to 12.5 kHz. The composite was then strained and an intrinsic frequency was observed which had a linear dependence on the strain with a frequency shift of 84 Hz / % strain. Lastly the composite was used in a strain-tuned amplifier circuit and shown to provide a gain of up to 4.5. This thesis provided the groundwork for a completely flexible electronically active device for futuristic bio-electronic skins with resolutions and sensitivities rivalling those of human tactile sensing.

The primary subject of this thesis is graphene and how the rudimentary attributes of its charge carriers, and local moments on its surface, can be directly manipulated and controlled with electrostatic potentials. We first consider bilayer graphene subject to a spatially varying electrostatic potential that forms two neighbouring regions with opposite interlayer bias. Along the boundary, 1D chiral `kink' states emerge. We find that these 1D modes behave as a strongly interacting Tomonaga-Luttinger liquid whose properties can be tuned via an external gate. Next, we consider superlattices in bilayer graphene. Superlattices are seen to have a more dramatic effect on bilayer graphene than monolayer graphene because the quasiparticles are changed in a fundamental way; the dispersion goes from a quadratic band touching point to linearly dispersing Dirac cones. We illustrate that a 1D superlattice of either the chemical potential or an interlayer bias generates multiple anisotropic Dirac cones. General arguments delineate how certain symmetries protect the Dirac points. We then map the Hamiltonian of an interlayer bias superlattice onto a coupled chain model comprised of `topological' edge modes. We then discuss the relevance of spatially varying potentials to recent transport measurements. This is followed by another study that considers the effect of a magnetic field on graphene superlattices. We show that magnetotransport measurements in a weak perpendicular (orbital) magnetic field probe the number of emergent Dirac points and reveal further details about the dispersion. In the case of bilayer graphene, we also discuss the properties of kink states in an applied magnetic field. We then consider the implications of these results with regards to scanning tunnelling spectroscopy, valley filtering, and impurity induced breakdown of the quantum Hall effect. Finally, we investigate local moment formation of adatoms on bilayer graphene using an Anderson impurity model. We construct various phase diagrams and discuss their many unusual features. We identify regions where the local moments can be turned on or off by applying a external electric fields. Finally, we compute the RKKY interaction between local moments and show how it too can be controlled with electric fields.

The primary subject of this thesis is graphene and how the rudimentary attributes of its charge carriers, and local moments on its surface, can be directly manipulated and controlled with electrostatic potentials. We first consider bilayer graphene subject to a spatially varying electrostatic potential that forms two neighbouring regions with opposite interlayer bias. Along the boundary, 1D chiral `kink' states emerge. We find that these 1D modes behave as a strongly interacting Tomonaga-Luttinger liquid whose properties can be tuned via an external gate. Next, we consider superlattices in bilayer graphene. Superlattices are seen to have a more dramatic effect on bilayer graphene than monolayer graphene because the quasiparticles are changed in a fundamental way; the dispersion goes from a quadratic band touching point to linearly dispersing Dirac cones. We illustrate that a 1D superlattice of either the chemical potential or an interlayer bias generates multiple anisotropic Dirac cones. General arguments delineate how certain symmetries protect the Dirac points. We then map the Hamiltonian of an interlayer bias superlattice onto a coupled chain model comprised of `topological' edge modes. We then discuss the relevance of spatially varying potentials to recent transport measurements. This is followed by another study that considers the effect of a magnetic field on graphene superlattices. We show that magnetotransport measurements in a weak perpendicular (orbital) magnetic field probe the number of emergent Dirac points and reveal further details about the dispersion. In the case of bilayer graphene, we also discuss the properties of kink states in an applied magnetic field. We then consider the implications of these results with regards to scanning tunnelling spectroscopy, valley filtering, and impurity induced breakdown of the quantum Hall effect. Finally, we investigate local moment formation of adatoms on bilayer graphene using an Anderson impurity model. We construct various phase diagrams and discuss their many unusual features. We identify regions where the local moments can be turned on or off by applying a external electric fields. Finally, we compute the RKKY interaction between local moments and show how it too can be controlled with electric fields.

The ability to isolate single atomic layers of van der Waals materials has led to renewed interest in the electronic and optical properties of these materials as they can be fundamentally different at the monolayer limit. Moreover, these 2D crystals can be assembled together layer by layer, with controllable sequence and orientation, to form artificial materials that exhibit new features that are not found in monolayers nor bulk. Twisted bilayer graphene is one such prototype system formed by two monolayer graphene layers placed on top of each other with a twist angle between their lattices, whose electronic band structure depends on the twist angle. This thesis presents the efforts to explore the electronic and optical properties of twisted bilayer graphene by Raman spectroscopy and scanning tunneling microscopy measurements. We first synthesize twisted bilayer graphene with various twist angles via chemical vapor deposition. Using a combination of scanning tunneling microscopy and Raman spectroscopy, the twist angles are determined. The strength of the Raman G peak is sensitive to the electronic band structure of twisted bilayer graphene and therefore we use this peak to monitor changes upon doping. Our results demonstrate the ability to modify the electronic and optical properties of twisted bilayer graphene with doping. We also fabricate twisted bilayer graphene by controllable stacking of two graphene monolayers with a dry transfer technique. For twist angles smaller than one degree, many body interactions play an important role. It requires eight electrons per moire unit cell to fill up each band instead of four electrons in the case of a larger twist angle. For twist angles smaller than 0.4 degree, a network of domain walls separating AB and BA stacking regions forms, which are predicted to host topologically protected helical states. Using scanning tunneling microscopy and spectroscopy, these states are confirmed to appear on the domain walls when inversion symmetry is broken with an external electric field. We observe a double-line profile of these states on the domain walls, only occurring when the AB and BA regions are gaped. These states give rise to channels that could transport charge in a dissipationless manner making twisted bilayer graphene a promising platform to realize controllable topological networks for future applications.

There is a movement in the electronic industry toward building electronic devices with dimensions smaller than is currently possible. Atomically thin 2D material, such as graphene, bilayer graphene, hBN and MoS2 are great candidate for this goal and they have a potential set of novel electronic properties compare to their bulk counterparts due to the exhibition of quantum confinement effects. To this goal, we have investigated the electric field screening of multilayer 2D materials due to the presence of impurity charge in the interface and vertical electric fifield from back gate. Our result shows a dramatic difference of screening behavior in high and low charging limit, which depends on the number of layers as well. We also have an extensive study on quantum tunneling effect in graphene and bilayer graphene heterojunctions. The peculiar electronic properties of graphene lead to an unusual scattering effect of electron in graphene n-p junction. We implement the cohesive tunneling effect to explain the nonlinear electron transport in ultrashort channel graphene devices. This nonlinear behavior could make them tremendously useful for ultra-fast electronic applications.