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Graphene is a recently created truly two-dimensional carbon material with promising properties. It is a prospective candidate for the next generation of microelectronics. Current carriers in graphene have relativistic properties, its lattice is very strong and yet flexible, granting graphene's ballistic conductivity on the submicron scale at the room temperatures. Midgap bound state induced by a single impurity in graphene does not cause essential changes in the electronic liquid distribution at all reasonable values of the coupling strength. Thus there are no unusual screening effects predicted for the graphene with long-range Coulomb impurity. This result holds in case of multiple impurities localized in the finite area on the lattice. Exact expressions for the lattice Green functions are derived. The absence of critical screening for the short-range impurities in graphene is a main result of the work. Another outcome is the observation of the limitations on the Dirac approximation applicability. / Micro-Electro-Mechanical Systems and Nanosystems

No description available.

No description available.

This thesis is devoted to quantum confinement effects in low-dimensional Dirac materials. We propose a variety of schemes in which massless Dirac fermions, which are notoriously diffcult to manipulate, can be trapped in a bound state. Primarily we appeal for the use of external electromagnetic fields. As a consequence of this endeavor, we find several interesting condensed matter analogues to effects from relativistic quantum mechanics, as well as entirely new effects and a possible novel state of matter. For example, in our study of the effective Coulomb interaction in one dimension, we demonstrate how atomic collapse may arise in carbon nanotubes or graphene nanoribbons, and describe the critical importance of the size of the band gap. Meanwhile, inspired by groundbreaking experiments investigating the effects of strain, we propose how to confine the elusive charge carriers in so-called velocity barriers, which arise due to a spatially inhomogeneous Fermi velocity triggered by a strained lattice. We also present a new and beautiful quasi-exactly solvable model of quantum mechanics, showing the possibilities for confinement in magnetic quantum dots are not as stringent as previously thought. We also reveal that Klein tunnelling is not as pernicious as widely believed, as we show bound states can arise from purely electrostatic means at the Dirac point energy. Finally, we show from an analytical solution to the quasi-relativistic two-body problem, how an exotic same-particle paring can occur and speculate on its implications if found in the laboratory.

Abstract The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooper-pair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a current-biased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.

We have studied the electron quantum phase by fabricating low dimensional (d ≤ 2) mesoscopic interferometers in high-quality narrow-gap semiconductor (NGS) heterostructures. The low effective-mass electrons in NGS heterostructures enable observation of delicate quantum phases; and the strong spin-orbit interaction (SOI) in the systems gives us means by which we can manipulate the quantum-mechanical spin of these electrons through the orbital properties of the electrons. This enables the observation of spin-dependent phenomena otherwise inaccessible in non-magnetic systems. We have performed low temperature (0.4 K ≤ T ≤ 8 K), low noise (â V ~ 1μV ) transport measurements, and observed evidence of Aharonov-Bohm (AB) and Alâ tshuler-Aronov-Spivak (AAS) quantum oscillations in meso- scopic devices that we fabricated on these NGSs. Our measurements are unique in that we observe both AB and AAS in comparable magnitude in ballistic networks with strong SOI. We show that, with appropriate considerations, diffusive formalisms can be used to describe ballistic transport through rings, even in the presence of SOI. This work also contains an introduction to the physics of geometric phases in mesoscopic systems, and the experimental and analytic processes through which these phases are probed. A discussion of the results of our measurements presents the case that quantum interferometric measurements of geometric phases can be understood quite thoroughly, and that these measurements may have deeper utility in discovery than has yet been recognized. / Ph. D.

Electron transport in mesoscopic systems, such as quantum point contacts and Aharonov-Bohm rings are investigated numerically in a tight-binding language with a recursive Green's function algorithm. The simulation reveals among other things the quantized nature of the conductance in point contacts, the Hall conductance, the decreasing sensitivity to scattering impurities in a magnetic field, and the periodic magnetoconductance in an Aharonov-Bohm ring. Furthermore, the probability density distributions for some different setups are mapped, making the transmission coefficients, the quantum Hall effect, and the cyclotron radius visible, where the latter indicates the correspondance between quantum mechanics and classical physics on the mesoscopic scale.

Cette thèse est consacrée à l'étude du transport dans les nanostructures quantiques unidimensionnelles dont les propriétés sont étudiées en s'appuyant notamment sur le bruit en excès à fréquence finie. La première partie de cette thèse est consacrée à l'étude du transport à travers une impureté dans un liquide de Luttinger couplée à un environnement électromagnétique arbitraire. L'impureté est traitée dans deux limites de transmission, la limite tunnel et la limite de faible rétrodiffusion. Les calculs sont menés dans le formalisme de Keldysh. Nous montrons ainsi que la théorie du blocage de Coulomb dynamique, établie pour une jonction tunnel couplée à un environnement à l'équilibre, demeure valide pour un liquide de Luttinger. Par ailleurs nous montrons que les relations de fluctuation dissipation reliant le bruit à fréquence finie au courant reste valide. Nous montrons que cette théorie peut également s'étendre dans la limite de faible rétrodiffusion à condition de prendre en compte la rétro-action du liquide électronique sur l'environnement. En revanche, les relations de fluctuation dissipation ne sont respectées que pour le bruit en émission. Dans une seconde partie nous intéressons effets d'une modulation radiofréquence sur les propriétés de transport des mêmes systèmes. Nous montrons notamment que ces effets peuvent être décrit par une théorie du blocage de Coulomb dynamique effective en convoluant la statistique d'absorption de photon avec la statistique de Tien-Gordon. Notons cependant que les relations de fluctuation dissipation ne sont plus vérifiées. Ces prédictions théoriques sont comparées aux résultats expériments obtenus par une équipe du SPEC au CEA de Saclay. Enfin nous étudions les propriétés de transport lorsque l'environnement, ici un oscillateur harmonique, est maintenu dans un état excité. Nous montrons que la présence de photons autorise d'une part le processus photo-assistés mais favorise également l'absorption de photons par des processus de bunching. Nous montrons finalement que les propriétés du transport s'obtiennent en convoluant la loi de Poisson du blocage de Coulomb avec la fonction caractéristique de Glauber de l'état peuplant l'oscillateur, menant à des statistiques exotiques. Ce dernier point nous permet d'utiliser ce système comme un détecteur d'état quantique. / This thesis discusses electronic transport in uni-dimensional quantum systems whose properties are studied with an extensive use of the finite-frequency non symmetrised excess noise. The first part focuses on transport through an impurity embedded in a Luttinger liquid coupled to an arbitrary electromagnetic environment. The impurity is treated in two paradigmatic situations : The tunneling and the weak backscattering regime. The out-of-equilibrium situation is dealt with the Keldysh Formalism. We show that the dynamical Coulomb blockade theory, extends to the case of a a tunnel junction between Luttinger liquids. Besides, fluctuations dissipation relations that link noise noise and current remain valid. In the transparent regime, we show that the dynamical Coulomb blockade theory applies to the backscattering current albeit back-action effects of the electronic liquid on the electromagnetic environment that have to be taken into account. Fluctuation-dissipation relations remain valid only for the emission noise. The second part focuses on the effects of a micro-wave modulation on the transport properties of the transport properties of these systems. An effective dynamical Coulomb blockade can be obtained by convolving the statistic of absorption of the environment with the Tien-Gordon statistic. Yet, the fluctuation dissipation relations are not verified in this case. These predictions are compared to the experimental results obtained by a team of the SPEC at the CEA Saclay. Last, we study the transport properties of a tunnel junction coupled to a harmonic oscillator maintained in an excited state. We show that the photons within the cavity lead to two distinct processes: photo-assisted transport that enhance the conductance, and bunching effects that enhance the probability to absorbe a large number of photons. An effective dynamical Coulomb blockade theory can also be derived by convolving the Poisson distribution with Glauber characteristic function leading to exotic statistics. These can be probed by excess noise which can thus be used as a quantum state detector.

This work explores the effects of weak nonlinearity on harmonic oscillators.Two particular systems are studied experimentally: A superconductingresonator formed from a coplanar waveguide that oscillates at microwave frequencies,and the cantilever of an atomic force microscope (AFM) vibratingat ultrasonic frequencies. Both of these systems are described in the introduction,followed by a theory chapter giving a general theoretical framework for nonlinear oscillators. Basic properties of nonlinear oscillators, such asbifurcation and intermodulation, are explained using simple models. Experimental methods, including cryogenic and microwave measurement techniques,are described in some detail. The nonlinear superconducting resonator is studied for use as a parametric amplifier. A strong drive tone, called the pump, drives the oscillator nearthe point of bifurcation. A second, much weaker drive signal that is slightlydetuned from the pump, will cause energy to move from the pump to the signal, giving signal amplification. We have measured a signal gain greaterthan 22 dB in a bandwidth of 30 kHz, for a resonator pumped at 7.6 GHz.This type of amplifier is phase-sensitive, meaning that signals in phase withthe pump will be amplified, but signals in quadrature phase of the pump will be deamplified. Phase-sensitivity has important implications on the amplifier’snoise properties. With a parametric amplifier, a signal can be amplified without any additional noise being added by the amplifier, something that is fundamentally impossible for a standard amplifier. The vibrating AFM cantilever becomes a nonlinear oscillator when it is interacting with a surface. When driven with two frequencies, the amplitudeand phase of the cantilever’s response will develop mixing products, or intermodulation products, that are very sensitive to the exact form of the nonlinearity. Very small changes in the surface properties will be detectable when measuring the intermodulation products. Simultaneously measuring many intermodulation products, or acquiring an intermodulation spectrum,allows one to reconstruct the tip-surface interaction. Intermodulation AFM increases the sensitivity of the measurement or the contrast of the acquiredimages, and provides a means of rapidly measuring the nonlinear tip-surface interaction. The method promises to enhance the functionality of the AFM beyond simple topography measurement, towards quantitative analysis of the chemical or material properties of the surface. / <p>QC 20100812</p>