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  • 1.
    Gustafsson, Alexander
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Electron transport in quantum point contacts: A theoretical study2011Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    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.

  • 2.
    Gustafsson, Alexander
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Quantum point contact: A theoretical study2010Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Experiments shows that the conductance of a quantum point contact is quantized in steps of  2e²/h, where e is the charge of the electron and h is Planck’s constant, and thereby Ohm’s law is not valid for nanostructures. By using the approximation method finite difference, the transmission for one-dimensional contacts and one- and two-dimensional potentials are investigated. In the case of two-dimensional contacts and a two-dimensional potential the Green’s function method is used. It turns out that if electrons are treated as waves, the transmission and the conductance just differ by the constant 2e²/h, which in this thesis is interpreted numerically in Matlab by using the Green’s function method.

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