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Sohrmann, Christoph
Languages: English
Types: Doctoral thesis
Subjects: QC
This thesis captures a numerical study of the interplay between disorder and electron-electron interactions within the integer quantum Hall effect, a regime where the presence of a strong magnetic field and two-dimensional confinement of the electrons profoundly affects the electronic properties. Prompted by recent novel experimental results, we particularly emphasise the behaviour of the electronic compressibility as a joint function of magnetic field and electron density, which appears to be insufficiently accounted for by the widely used independent-particle model. Our treatment of the electron-electron interactions relies on the Hartree-Fock approximation so as to achieve system sizes comparable to the experimental situation. We find numerical evidence for various interaction-mediated effects, such as non-linear screening, local charging, and g-factor enhancement. Important implications for the phase diagram may arise, although a study of the scaling of the participation ratio seems to imply a universal critical behaviour independent of interactions. Furthermore, we examine the Hall conductivity in a similar fashion, which also displayed interaction-promoted features in transport measurements. Our mesoscopic simulations only reproduce some of the observed features, suggesting the presence of effects beyond numerical tractability. Finally, we model scanning tunneling spectroscopy experiments and systematically investigate the influence of the tip induced potential as well as the interactions among the electrons. Our results show a strong dependence on the filling factor and may greatly assist the interpretation of such spectroscopy data.
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