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Electronic systems subject to competing interactions can end up in different phases as the balance between these interactions shifts. When a quantum critical point separates these phases, exotic electronic behavior often marks the vicinity of the transition. In this work, we construct nanopatterned devices to probe such critical phenomena. The basic element of our devices is the GaAs/AlGaAs quantum dot, an isolated region of electronic charge which is coupled to a two-dimensional gas of weakly interacting electrons. We use different designs of quantum dots to realize different models. The first device studied in this work realizes the spin two-channel Kondo ('spin 2CK') model. In this model, a single impurity (i.e. a single spin-degenerate dot) is coupled to two separate reservoirs. When the couplings to both reservoirs are unequal, the more strongly coupled reservoir screens the impurity spin degeneracy and forms a many-body singlet; this is known as the Kondo effect. When both reservoirs are coupled equally strongly, a non-Fermi liquid ground state arises as a result of the overscreening by both reservoirs. We probe the anomalous scaling properties of this state, and show how it transitions into a more conventional Fermi liquid under the influence of various perturbations. The second device is first operated as a single metallic quantum dot in the quantum Hall regime. Spin degeneracy is broken, but the device can be tuned such that there is now a charge degeneracy which can then be screened by coupling to a reservoir. We tune to and away from equal couplings to see the effect of the two-channel Kondo state. Finally, we operate the second device in its full form as a double-dot device, to explore the competition between dot-lead and interdot interactions.
Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit
We study correlated two-level quantum impurity models coupled to a metallic con- duction band in the hope of gaining insight into the physics of nanoscale quantum dot systems. We focus on the possibility of formation of a spin-I impurity local moment which, on coupling to the band, generates an underscreened (USC) singular Fermi liq- uid state. By employing physical arguments and the numerical renorrnalization group (NRG) technique, we analyse such systems in detail examining in particular both the thermodynamic and dynamic properties, including the differential conductance. The quantum phase transitions occurring between the USC phase and a more ordinary Fermi liquid (FL) phase are analysed in detail. They are generically found to be of Kosterlitz- Thouless type; exceptions occur along lines of high symmetry where first-order transitions are found. A 'Friedel-Luttinger sum rule' is derived and, together with a generalization of Luttinger's theorem to the USC phase, is used to obtain general results for the T = 0 zero-bias conductance ~ it is expressed solely in terms of the number of electrons present on the impurity and applicable in both the USC and FL phases. Relatedly, dynamical signatures of the quantum phase transition show two broad classes of behaviour corresponding to the collapse of either a resonance or antiresonance in the single-particle density of states. Evidence of both of these behaviours is seen in experimental devices. We study also the effect of a local magnetic field on both single- and two-level quantum impurities. In the former case we attempt -to resolve some points of con- tention that remain in the literature. Specifically we show that the position of the maximum in the spin resolved density of states (and related peaks in the diffcrcn- tial conductance) is not linear in the applied field, showing a more complicated form than a simple 'Zeeman splitting'. The analytic result for the low-field asymptote is recovered. For two-level impurities we illustrate the manner in which the USC sta.te is destroyed: due to two cancelling effects an abrupt change in the zero-bias conductance does not occur as one might expect. Comparison with experiment is made in both cases and used to interpret experimental findings in a manner contrary to previous suggestions. We find that experiments are very rarely in the limit of strong impurity- host coupling. Further, features in the differential conductance as a function of bias voltage should not be simply interpreted in terms of isolated quantum dot states. The many-body nature of such systems is crucially important to their observed properties.
The exciting field of nanostructured materials offers many challenging perspectives for fundamental research and technological applications. The combination of quantum mechanics, interaction, phase coherence, and magnetism are important for understanding many physical phenomena in these systems. This book provides an overview of many aspects of interacting electrons in nanostructures, including such interesting topics as quantum dots, quantum wires, molecular electronics, dephasing, spintronics, and nanomechanics. The content reflects the current research in this area and is written by leading experts in the field.
A quantum dot molecule (QDM) is composed of two or more closely spaced quantum dots or “artificial atoms.” In recent years, QDMs have received much attention as an emerging new artificial quantum system. The interesting and unique coupling and energy transfer processes between the “artificial atoms” could substantially extend the range of possible applications of quantum nanostructures. This book reviews recent advances in the exciting and rapidly growing field of QDMs via contributions from some of the most prominent researchers in this scientific community. The book explores many interesting topics such as the epitaxial growth of QDMs, spectroscopic characterization, and QDM transistors, and bridges between the fundamental physics of novel materials and device applications for future information technology. Both theoretical and experimental approaches are considered. Quantum Dot Molecules can be recommended for electrical engineering and materials science department courses on the science and design of advanced and future electronic and optoelectronic devices.
The thesis presents the results of the Numerical Renormalization Group (NRG) approach to three impurity models centered on the issues of impurity quantum phase transitions. The soft-gap Anderson model is one of the most well-established cases in the contexts of impurity quantum phase transitions and various analytic and numerical methods examined the physical properties of the quantum critical phase as well as the stable phases on both sides of the transition point. Our contribution is made to the former case by analyzing the NRG many-particle spectrum of critical fixed points, with which we can see how the impurity contribution of the thermodynamic quantities have fractional degrees of freedom of charge and spin. The quantum phase transition of the spin-boson model has a long history but most of achievements were reached for the ohmic dissipation. The new development of the NRG treating the bosonic degrees of freedom broadened the range of the parameter space to include the sub-ohmic case and, as a result, second order phase transitions were found for the bath exponent $0
Since first developed in the early sixties, silicon chip technology has made vast leaps forward. From a rudimentary circuit with a mere handful of transistors, the chip has evolved into a technological wonder, packing millions of bits of information on a surface no larger that a human thumbnail. And most experts predict that in the near future, we will see chips with over a billion bits. Quantum dots are small devices that contain a tiny droplet of free electrons. They are fabricated in semiconductor materials and have typical dimensions ranging from nanometres to a few microns. The size and shape of these structures and therefore the number of electrons they contain can be precisely controlled; a quantum dot can have anything from a single electron to a collection of several thousands. The physics of quantum dots shows many parallels with the behaviour of naturally occurring quantum systems in atomic and nuclear physics. As in an atom, the energy levels in a quantum dot become quantised due to the confinement of electrons. Unlike atoms however, quantum dots can be easily connected to electrodes and are therefore excellent tools for studying atomic-like properties. This new book brings together leading research from throughout the world in this field of the future which has become the field of today.
The book reflects scientific developments in the physics of metallic compound based nanodevices presented at the NATO-sponsored Workshop on nanophysics held in Russia in the summer of 2003. The program tackles the most appealing problems. It brings together specialists and provides an opportunity for young researchers from the partner countries to interact with them and get actively involved in the most attractive and promising interdisciplinary area of contemporary condensed matter physics.