Browsing by Author "Schulz, Leonhard"

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    Parallel arrangements of quantum dots and quantum point contacts in high magnetic fields : periodic conductance modulations with magnetic flux change
    (2014) Schulz, Leonhard; von Klitzing, Klaus (Prof. Dr.)
    Within the general framework of quantum physics all objects acquire wave character, inherently enabling interference. For electrons one of the first interferometry experiments used a double-slit, as one particular realization of a more general class of two-path arrangements. Since electrons are charged, their interference is susceptible to the presence of a magnetic flux, known as the Aharonov-Bohm effect. By changing the magnetic flux one obtains a periodic h/e shift of the interference fringes. Further experiments trying to investigate the Aharonov-Bohm effect utilized two-dimensional electron systems (2DES) in solid state devices such as (Al,Ga)As-heterostructures. With state-of-the-art micro-lithography patterning techniques various paths arrangements guiding the electrical current can be realized. It furthermore allows to include more elaborate elements within these loops showing quantum mechanical effects themselves, such as quantum point contacts or quantum dots. In this PhD work Aharonov-Bohm-like conductance modulations in two-path arrangements, built from two-dimensional electron systems tuned to the regime of the quantum Hall effect (QHE), were investigated. These are usually interpreted as interference in the so-called edge state picture of the QHE. Three different two-path configurations were addressed: two parallel constrictions, two parallel quantum dots and their intermediate combination of a single constriction and a quantum dot. The quantum Hall effect is thereby thought to give rise to an additional confinement of the current distribution within the 2DES. However, an accurate microscopic picture has to be applied. The key element of understanding the current distribution is the formation of the so-called electrically compressible and incompressible landscape, contradicting the current distribution within the edge-state model. The compressible/ incompressible picture is validated as true microscopic picture by scanning-force microscopy experiments. It has been already shown, that the h/e periodic conductance modulations seen in the arrangement of two parallel constrictions do not arise from an Aharonov-Bohm like interference effect. They rather emerge from single-electron tunneling between the compressible edges of the Hall device via a compressible strip present around a central antidot. Thus, reducing the Hall-voltage drop and inherently the Hall-current flowing through the device. Smaller integer fractions of h/e can be observed in the presence of spatially separated compressible annuli. Here, we observed an h/2e periodicity. As spatial separation cannot be assumed in our case, we have developed a model for the presence of a spin-degenerate compressible strip around the antidot allowing to observe the halved h/2e periodic conductance modulations as well. In addition, we found a scaling of the magnitude of the conductance modulations in between h/e and h/2e periodicity. It is expected within the picture of the compressible/ incompressible landscape, but hardly explainable within the picture of interfering edge-states. A new arrangement in this thesis is the combination of two quantum dots. Here the electrical current is maintained by single-electron tunneling events, thought to mimic a double-slit in a solid. Although we observed h/e periodic conductance modulations, no evidence of (destructive) interference as underlying mechanism was found. Instead, we identified that a breathing of a closed wave function connected throughout the two quantum dots - altering the individual tunneling barriers - is the origin of the periodic conductance modulations. In addition, experiments were conducted for the Kondo regime of the quantum dots. Here, in the presence of a spin degeneracy, a change to an h/2e periodic conductance modulations was observed. For the intermediate configuration with a constriction and a single quantum dot we showed again both the h/e and h/2e periodicity of the conductance modulations. The latter being thereby observable only in the presence of a spin-degeneracy in either device part. In addition, we substantiate the presence of the closed wave function from the 180° phase shift in the periodic conductance modulations when tuning the quantum dot through the resonance of a single-electron tunneling resonance level. In summary, interference can be excluded as the cause of the periodic conductance modulations for all three configurations examined in this work. Instead, treating the electrostatics of the system self-consistently in the presence of a closed and possibly spin-degenerate wave function accounts for all experimental observations.