27 research outputs found

    Magnetoresistance in Disordered Graphene: The Role of Pseudospin and Dimensionality Effects Unraveled

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    We report a theoretical low-field magnetotransport study unveiling the effect of pseudospin in realistic models of weakly disordered graphene-based materials. Using an efficient Kubo computational method, and simulating the effect of charges trapped in the oxide, different magnetoconductance fingerprints are numerically obtained in system sizes as large as 0.3 micronmeter squared, containing tens of millions of carbon atoms. In two-dimensional graphene, a strong valley mixing is found to irreparably yield a positive magnetoconductance (weak localization), whereas crossovers from positive to a negative magnetoconductance (weak antilocalization) are obtained by reducing disorder strength down to the ballistic limit. In sharp contrast, graphene nanoribbons with lateral size as large as 10nm show no sign of weak antilocalization, even for very small disorder strength. Our results rationalize the emergence of a complex phase diagram of magnetoconductance fingerprints, shedding some new light on the microscopical origin of pseudospin effects.Comment: 8 pages, 5 figure

    Quantum transport in nanostructures: From the effects of decoherence on localization to magnetotransport in two-dimensional electron systems

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    In this thesis, quantum transport in nanostructures is studied theoretically by means of the nonequilibrium Green's function (NEGF) method. Starting with coherent systems, we discuss ballistic transport and conductance quantization in homogeneous tight-binding lattices. We show that disorder gives rise to transmission resonances. A short introduction to Anderson localization is given and a compact analytical formula for the disorder averaged resistance is derived by means of generating functions. Transport in nanostructures generally takes place in an intermediate regime between quantum and classical transport due to decoherence. We study the effects of decoherence on electron transport by a statistical model. The essential idea of our model is to distribute spatially over the system decoherence regions, where phase and momentum of the electrons are randomized completely. The transport in between these regions is assumed as phase coherent. Afterwards, the transport quantity of interest is ensemble averaged over spatial decoherence configurations, which are generated according to a given distribution function. We discuss how homogeneous tight-binding lattices are driven by decoherence from the quantum-ballistic to the classical-Ohmic regime. We show that the transport through disordered tight-binding lattices is affected significantly by the spatial distribution of the decoherence regions. If the decoherence is homogeneously distributed, Ohmic conduction is found for any finite degree of decoherence. In contrast, for randomly distributed decoherence, we find an insulator-metal transition from the localized to the Ohmic regime at a critical degree of decoherence, which corresponds to a critical phase coherence length. We also discuss how transport in disordered tight-binding lattices can be enhanced by decoherence. The decoherence model is extended to obtain pure dephasing. We show that transmission resonances are suppressed by pure dephasing, but the average transmission is conserved. The insulator-metal transition is independent of whether phase randomization goes along with momentum randomization or not. Magnetotransport in two-dimensional electron systems is considered. We study how electrons, coherently injected at one point on the boundary of a two-dimensional electron gas (2DEG), are focused by a perpendicular magnetic field onto another point of that boundary. At weak magnetic field, the generalized 4-point Hall resistance shows equidistant peaks, which can be explained by classical cyclotron motion. When the magnetic field is increased, we observe anomalous resistance oscillations superimposed upon the quantum Hall plateaus. We show that all resistance oscillations can be explained by the interference of the occupied edge channels. The anomalous oscillations are beatings, which appear when only some few edge channels are occupied. By introducing decoherence and partially diffusive boundary scattering, we show that this effect is quite robust. The resistance oscillations can be observed not only in a nonrelativistic 2DEG, but also in the relativistic 2DEG found in graphene. We also report a finite current at armchair edges of graphene ribbons, which is not present at zigzag edges. This edge current can be traced back to the fact that at armchair edges carbon atoms of both graphene sublattices are present, whereas at zigzag edges only atoms of one sublattice appear. The thesis is concluded with some notes on Hofstadter's butterfly shown on the cover page

    Electronic transport in two dimensional graphene

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    We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical transport are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long- range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, p-n junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.Comment: Final version as accepted for publication in Reviews of Modern Physics (in press), 69 pages with 38 figure

    Magnéto-transport dans les nanorubans de graphène

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    Dans ce travail de thèse, nous étudions les propriétés de transport électronique des nanorubans de graphène sous champs magnétiques intenses (jusqu'à 55 T) pour révéler les effets de confinements électroniques dans la structure de bande de graphène. Les nanorubans de graphène (GNRs) sont des matériaux prometteurs pour la nanoélectronique à base de carbone, qu'il s'agisse d'interconnection ou bien de dispositifs actifs pour l'electronique logique ou radiofréquence. Lorsque graphène est structurée à une échelle nanométrique, avec un contrôle précis de la symétrie des bords, il est possible d'ouvrir un gap d'énergie dans la structure de bande et de moduler le nombre de canaux de conductance par un couplage électrostatique local. Malheureusement, une telle ingénierie du gap s'accompagne d'un contrôle delicat de la qualité des bords et, par conséquence, d'une baisse drastique de la mobilité électronique. La plupart des effets du confinement sur la structure électronique sont alors masqués par la présence de désordre. La preuve expérimentale de la structure de bande électronique intrinsèque des GNRs reste un veritable challenge. Ici, nous démontrons que sous l'effet d'un grand confinement magnétique et ceux, malgré la présence de désordre, nous révélons des spectres Landau anormals, signatures du confinement électronique dans les GNRs. Les expériences de magnéto-transport sont principalement realiséess en GNRs monocouches sur Si/SiO2, conçus par lithographie électronique et gravure ionique réactive, avec des largeurs nominales comprises entre 55 et 100 nm. La mobilité des porteurs varie de 600 à 3500 cm2 V-1 s-1. Pour les plus larges GNRs (~100 nm), présentant un régime faiblement diffusive, nous apportons la preuve, à forts niveaux de dopage, des anomalies dans les oscillations Shubnikov-de Haas, due au confinement électronique. A niveau de dopage plus faible, nous observons une quantification de la conductance en regime de Landau, avec des facteurs de remplissage attendus pour le graphène. Pour les GNRs les plus étroits, de nouvelles oscillations quantiques se développent dans le régime de Landau. Ce spectre singulier, directement comparé aux calculs des sous-bandes magnéto-électriques, est attribué à une levée de dégénérescence de vallée induite par le confinement en présence d'une symétrie de type armchair sur les bords Nous présentons egalement des résultats de transport electronique sous champs magnétiques intenses obtenus sur des nanorubans de graphène bicouche et nous les comparons au magnéto-transport realisé sur des bicouches graphène non structurées. La comparaison revéle de nouvelles magnéto-signatures dans les GNRs bicouche, provenant des effets de confinement électroniques. Comme partie complémentaire, nous étudions enfin la cohérence de phase dans les GNRs; celle-ci se manifeste par des fluctuations de conductance induites par un champ magnétique ou une tension de grille appliquée à l'échantillon. Nous nous concentrons principalement sur les fluctuations de conductance dans le régime hors équilibre. L'analyse des amplitudes et de la tension de corrélation donne accés à la longueur de cohérence de phase et met en evidence le role preponderant des interactions électron-électron comme mécanisme responsable de la décohérence. Finalement, nous étudions la réponse du graphène à un rayonnement THz. Les expériences montrent une corrélation forte entre la photo-réponse et le second harmonique des fluctuations de conductance. Ceci ouvre une nouvelle possibilité d'étudie des effets mésoscopiques non linéaires utilisant des rayonnements THz.In the present PhD thesis, we study the electronic transport properties of grapheme nanoribbons under a large magnetic field (up to 55 T) to unveil the electronic confinement effects on the band structure of graphene. Graphene nanoribbons (GNRs) are promising materials to promote graphene for all carbon based nanoelectronics, including electronic wave guides and digital logic or radiofrequency devices. When graphene is structured at a nano-scale, with an accurate control of the edge symmetry, it is possible to open an energy gap in the band structure and to tune the number of conducting channels by a local electrostatic gate. Unfortunately, such a gap engineering goes along with a poor control of the edges' quality and, as a consequence, a drastic drop of the electronic mobility. Most of the confining potential effects on the band structure are masked by the presence of disorder and the experimental evidence of the intrinsic electronic band structure of GNR remains challenging. Here, we demonstrate that, by playing with a large magnetic confinement, we bring experimental evidence of anomalous Landau spectra, signature of the confining potential in GNRs. The magneto-transport experiments are mainly obtained on monolayer GNRs on Si/SiO2 substrates patterned by e-beam lithography and reactive ion etching, with nominal widths between 55 and 100 nm. The carrier mobility varies from 600 to 3500 cm2 V-1 s-1. For the largest GNR (~100 nm), presenting a weakly diffusive regime, we give evidence, at high doping levels, of anomalous Shubnikov-de Haas oscillations, fingerprint of the electronic confinement. At lower doping levels, we observe Landau quantization of the two probes conductance, for filling factor values expected for graphene. In narrower GNRs, new quantum oscillations develop in the quantum regime. This singular Landau spectrum, directly compared to magnetoelectric subbands calculations, is assigned to a possible valley degeneracy lifting driven by the confining potential in presence of armchair symmetry at the edges. Additionally, we present high magnetic field transport results obtained on bilayer graphene nanoribbons and we compare them to magneto-transport performed on un-structured graphene bilayer. The comparison unveils new magneto-signatures in bilayer GNRs, originating from the electronic confining effects. As a complementary part, we finally study the phase coherence in our GNR devices that manifests itself by magnetic field and back-gate voltage induced conductance fluctuations. We mainly focus on conductance fluctuations in the out-of-equilibrium regime. The analysis of the amplitude of the fluctuations and of the correlation voltage unveils the phase coherence length and its bias voltage dependence, signature of electron-electron interaction as the main mechanism responsible for the decoherence. Additionally, we investigate the response of graphene to a THz radiation. The experiments show a high cross correlation between the photo-response and the second harmonic conductance fluctuations of the electronic transport. This opens a new possibility to study non-linear mesoscopic effects using THz radiation

    Electronic and magnetic properties of selected two-dimensional materials

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    Electronic devices, such as field-effect transistors (FETs), based on low-dimensional materials attract an immense interest as a potential inexpensive, flexible and transparent next generation of electronics. There have been considerable improvements in the accessibility of various low-dimensional materials and even the first ferromagnetic monolayers have been experimentally realized. Nevertheless, many open questions remain concerning basic physical properties of such materials. This work focusses on the electronic and magnetic properties of three carefully selected and especially interesting low-dimensional materials: Bottom-up chemically synthesized graphene nanoribbons (GNRs), nitrogen-doped graphene films and ferromagnetic chromium trihalides. First, we investigate charge transport in bottom-up synthesized GNRs with various edge morphologies and ribbon widths. Although prototypes of FET devices based on such GNRs have recently been demonstrated, fundamental questions as for example on the dominant charge transport mechanism, or on the structure- and width-dependence of charge transport signatures in GNR devices, remain unanswered and need to be addressed experimentally. Therefore, we present the development of a reliable fabrication of GNR network FETs and their measurement. In devices with gold electrodes at micron and submicron channel lengths, we study length-dependent charge transport as a function of gate voltage and at a wide range of temperatures. First, we show that the contact resistance is low and behaves Ohmic-like. The channel current follows power laws for both temperature and drain voltage, which is explained by nuclear tunneling-mediated hopping as the dominant charge transport mechanism. In addition, we observe a large positive magnetoresistance of up to 14 % at magnetic fields of 8 T at low temperatures. We find this magnetoresistance only in GNRs which have a width of five carbon dimers across the ribbon and which are expected to exhibit a particularly low band gap. With our results we provide a better understanding of the nature of charge transport and the engineering of contacts, which both is evidently crucial to bolster any further development of GNR-based devices. Besides geometrical confinement in GNRs, we explore heteroatomic nitrogen doping as a second route of tailoring charge transport properties of graphene. Here, extended two-dimensional graphene films with substitutional nitrogen dopants are studied and compared to pristine graphene fabricated under identical conditions. By combining structural and electrical characterization methods, we elucidate the role of structural disorder and electron localization for the electronic properties of this material induced by the nitrogen dopants. We quantify the transition from weak to strong localization with doping level based on the change of the length scales for phase coherent transport. This transition is accompanied by a conspicuous sign change from positive ordinary Kohler magnetoresistance in undoped graphene to large negative magnetoresistance in doped graphene. In addition to charge carrier properties, also spin properties depend heavily on the dimensionality, where an important ingredient for stable magnetic order in lower dimensions is magnetic anisotropy. Therefore, we investigate chromium trihalides, which are layered and exfoliable semiconductors and exhibit unusual magnetic properties. In particular, we focus on the understanding of magnetocrystalline anisotropy by quantifying the anisotropy constant of chromium iodide (CrI3), where we find a strong change from 5 K towards the Curie temperature. We draw a direct comparison to chromium bromide (CrBr3), which serves as a reference, and where we find results consistent with literature. In particular, we show that the anisotropy change in the iodide compound is more than three times larger than in the bromide. We analyze this temperature dependence using a classical model for the behavior of spins and spin clusters showing that the anisotropy constant scales with the magnetization at any given temperature below the Curie temperature. Hence, the temperature dependence can be explained by a dominant uniaxial anisotropy where this scaling results from local spin clusters having thermally induced magnetization directions that deviate from the overall magnetization.Elektronische Bauteile auf Basis niedrigdimensionaler Materialien, wie zum Beispiel Feldeffekttransistoren (FETs), ziehen eine enorme Aufmerksamkeit auf sich und haben das Potential, die nächste Generation an kosteneffizienter, flexibler und transparenter Elektronik zu bilden. Es hat bereits eine bemerkenswerte Entwicklung im Bereich niedrigdimensionaler Materialien gegeben, sodass sogar die ersten ferromagnetischen Monolagen experimentell untersucht werden konnten. Nichtsdestotrotz sind viele grundlegenden physikalischen Eigenschaften unerforscht. Die vorliegende Arbeit beschäftigt sich mit den elektronischen und magnetischen Eigenschaften dreier niedrigdimensionaler Materialien: Chemisch bottom-up synthetisierte Graphennanobänder (GNRs), stickstoffdotierte Graphenfilme und ferromagnetische Chromtrihalogenide. Zuerst untersuchen wir Ladungstransport in bottom-up synthetisierten GNRs verschiedener Kantenmorphologien und Breiten. Obwohl erste FET-Prototypen basierend auf GNRs demonstriert wurden, sind einige fundamentale Fragen immer noch unbeantwortet und verlangen nach experimenteller Klärung. Diese Fragen betreffen zum Beispiel den Ladungstransportmechanismus oder die Struktur- und Breitenabhängigkeit des Ladungstransports. Daher präsentieren wir die technische Entwicklung einer verlässlichen Fabrikationsmethode von FETs basierend auf GNR-Netzwerken sowie die Charakterisierung dieser Bauteile. Als Funktion von Gatterspannung und für einen breiten Temperaturbereich untersuchen wir den längenabhängigen Ladungstransport mit Hilfe von FETs mit Goldelektroden und aktiven Kanälen im Bereich von einigen hundert Nanometern bis hin zu einigen Mikrometern. Dabei zeigen wir zunächst, dass der elektrische Kontaktwiderstand gering ist und sich ohmsch verhält. Desweiteren bestimmen Potenzgesetze das Verhalten des Kanalstroms in Abhängigkeit von Betriebsspannung und Temperatur, was mit Hilfe von kerntunnelnassistiertem Ladungsträgerhopping als maßgeblichen Ladungstransportmechanismus erklärt werden kann. Darüber hinaus finden wir einen ausgeprägten positiven Magnetowiderstand bis zu 14% bei Magnetfeldern von 8 T und tiefen Temperaturen. Diesen Magnetowiderstand finden wir ausschließlich in GNRs, die nur fünf Kohlstoffdimerlängen breit sind und bei welchen eine geringe Bandlücke erwartet wird. Mit unseren Ergebnissen tragen wir zu einem tieferen Verständnis des Ladungstransportmechanismus bei und zeigen die Optimierung der elektrischen Kontakte auf. Beides ist unerlässlich, um die Realisierung zukünftiger GNR-basierter Elektronik voranzutreiben. Neben der geometrischen Einschränkung von Ladungsträgern in GNRs, untersuchen wir Fremdatomdotierung mit Stickstoff als zweite Strategie Ladungstransport in Graphen maßzuschneidern. Dazu haben wir zweidimensionale Graphenfilme mit inkorporierter Stickstoffdotierung untersucht und vergleichen sie mit reinen Graphenfilmen, welche unter identischen Bedingungen hergestellt wurden. Indem wir strukturelle und elektronische Charakterisierungsmethoden miteinander verbinden, beleuchten wir die Rolle von struktureller Ungeordnetheit sowie elektronischer Lokalisierung, welche beide durch die Stickstoffdotierung induziert werden. Wir quantifizieren hierfür den, mit zunehmendem Dotierungsniveau einhergehenden, Übergang von schwacher zu starker Lokalisierung auf Grundlage der Änderung der Längenskala von phasenkohärentem Transport. Dieser Übergang wird begleitet von einer bemerkenswerten Vorzeichenänderung des Magnetowiderstands von gewöhnlichem Kohlermagnetowiderstand in undotiertem Graphen hin zu einem großen negativen Magnetowiderstand in dotiertem Graphen. Nicht nur das Verhalten von Ladungsträgern hängt von der Dimensionalität ab, sondern auch das von Spins. Hierbei ist magnetische Anisotropie ein wichtiger Faktor, um magnetische Ordnung in niedrigen Dimensionen zu erklären. Daher untersuchen wir als dritten Themenbereich die magnetischen Eigenschaften von Chromtrihalogeniden. Dies sind Halbleiterkristalle mit ungewöhnlichen magnetischen Eigenschaften und einer Schichtstruktur, wodurch sie sich zu Monolagen exfolieren lassen. Wir untersuchen insbesondere die magnetokristalline Anisotropie, indem wir die Anisotropiekonstante von Chromiodid (CrI3) als Funktion der Temperatur quantifizieren. Wir beobachten dabei eine starke Änderung der Anisotropie zwischen 5 K und der Curie-Temperatur. Diese vergleichen wir mit der von Chrombromid (CrBr3), welches uns als Referenz dient, da es sich genauso verhält, wie es frühere, der Literatur entnommene, Untersuchungen erwarten lassen. Wir zeigen, dass bei gegebener Temperatur die Anisotropiekonstante mit der Magnetisierung skaliert und basierend auf einem klassischen Modell für das Verhalten der Spins erklären wir unsere experimentellen Beobachtungen mit einer dominant uniaxialen Anisotropie, bei welcher die Skalierung das Resultat von lokalen Spinclustern ist, deren Magnetisierungsrichtung durch thermische Aktivierung von der Ausrichtung der Gesamtmagnetisierung abweicht.xx, 180 Seite

    High-mobility graphene in 2D periodic potentials

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    This work focuses on hBN-graphene van der Waals heterostructures and their investigation via transport experiments. In this way, we could probe and characterize different commensurability effects stemming from the induced superlattice potential and report their influence on transport properties in graphene. The encapsulation of graphene between hBN significantly increases the bulk carrier mobility of graphene and were able to investigate interaction-driven quantum Hall effects, such as quantum Hall ferromagnetism and the fractional quantum Hall effect. Any further top-down patterning steps do not necessarily degrade the intrinsic quality of the graphene sheet. The high sample quality can be preserved in graphene-based antidot lattices and we successfully probed pronounced commensurability features in antidot arrays. Moreover, we study the interplay between a moiré and an imposed antidot superlattice potential and discuss their influence on magnetotransport measurements. In the end, we discuss a new method for imposing lateral superlattice potentials, employing a local few-layer graphene patterned bottom gate. In this way, we are able to report Weiss oscillations in the weakly modulated unipolar regime and antidot peaks for strong modulation in a bipolar gate configuration

    Hydrogen plasma etched graphene nanoribbons

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    Magnetic ordering in low dimensional semiconducting structures is an important element for spin-based electronics. Zigzag graphene nanoribbons which sustain ferromagnetic edge states and ordered nuclear magnetic states in GaAs 2DEGs are two such examples which represent potentials for spintronics applications. In order to be realized, both of these phenomena require certain conditions. For the magnetic ordering at the zigzag edges of graphene nanoribbons, fabrication of high quality edges is a prerequisite. Additionally, for the nuclear magnetic ordering in GaAs, the 2D system needs to reach below miliKelvin temperatures. Here, we study hydrogen plasma etching in graphite and graphene flakes in order to fabricate graphene nanoribbons with zigzag edges. We study the distance and pressure dependence of the etching process in graphite flakes, and define two distinct plasma regimes. The direct plasma regime contains high density of H radicals and energetic ions, which continuously induce defects on the surface, and results in perforated surfaces. On the other hand, the remote plasma regime includes only H radicals, giving the opportunity to take the etching process under control to fabricate graphene structures. The underlying substrate plays an important role in the etching process. For single layer flakes on hBN, the etching is highly anisotropic and creates hexagonal etch-pits, whereas on SiO2, the etching is isotropic. For bilayer flakes, the process is anisotropic on both subtrates. Atomic resolution atomic force microscopy reveals that the edges of the etched hexagons on graphite are parallel with the zigzag crystallographic direction and the absence of D-peak intensity in Raman spectra represents the high quality of the edges, since only armchair and disordered edges can result in D-peak intensity. However, for single layer samples on hBN, the high D-peak intensity shows that even tough the edges are along the zigzag direction, they are interrupted by symmetric armchair segments. Analysis on the polarization dependent Raman measurements result in the ratio of 40% for armchair segments along a zigzag edge. The picture of poor quality graphene edges is further confirmed by the low temperature transport measurements. None of the features predicted for electronic band structure of zigzag graphene nanoribbons are observed in the experiments. The findings are also supported by the tight-binding simulations for a disordered zigzag edge. In the second part of the thesis, we applied the well-established adiabatic nuclear demagnetization technique on a coulomb blockade thermometer in order to reach electron temperatures of below 1mK. In this experiment, each measurement lead is cooled by its own nuclear refrigerator made of 2mols of copper. The nuclei and charge carriers inside the coulomb blockade thermometer are cooled by large copper fins deposited on the chip. In order to investigate the efficiency of the process, we tested two different ramp-rates and precooling durations. Electron temperatures of 1.8mK and 2.7mK in the coulomb blockade thermometer are measured in two cool-downs, resulting in efficiencies of about 10%. A simple thermal model is given in the context of the measurements considering the heat leaks and thermal dynamics within the system, also comparing the results with previous experiments
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