The purpose of the present thesis is to investigate the effects of interactions in interferometers in the integer quantum Hall regime. The behaviour of electrons in condensed matter systems is mostly determined by the repulsive Coulomb interaction. However, under special circumstances the Coulomb interaction can be effectively attractive, giving rise to electron-pairing in unconventional superconductors and specifically designed mesoscopic setups. In particular, electron interactions can play a crucial role in quantum Hall systems, leading for instance to the emergence of quasi-particles with fractional charge and anyonic statistics. Quantum Hall Fabry-Pérot interferometers (FPI) have attracted increasing attention due to their ability to probe such exotic physics. In addition, such interferometers are affected by electron interactions themselves in unexpected ways. For example, experimental evidence for electron-pairing in a quantum Hall FPI was recently found. Interactions play a crucial role in quantum Hall FPI, and a deeper investigation of their effects is necessary in order to reach a better understanding of these systems.
We start by analysing the magnetic field and gate voltage dependence of the longitudinal resistance in an electronic FPI, taking into account the interactions between an outer-most interfering edge mode, an inner non-interfering edge mode and the bulk. For weak bulk-edge coupling and sufficiently strong inter-edge interaction, we obtain that the interferometer operates in the Aharonov-Bohm regime with a flux periodicity halved with respect to the usual expectation, as recently observed. We do not find evidence for a connection between a reduced flux period and electron pairing, though.
Then, we compute electron shot noise of an integer quantum Hall FPI in the limit of strong backscattering in the presence of a inter-edge repulsive interaction. We find that the Fano factor for strong edge-edge coupling is considerably enhanced with respect to the Fano factor of a non-interacting interferometer, indicating a significant correlation between the tunnelling of subsequent electrons. In particular, we find a two-fold enhanced Fano factor for some parameters, indicative of electron pairing as found experimentally. We interpret this result in terms of a dynamical attraction between electrons taking place in the interfering edge via the exchange of neutral inter-edge plasmons. We argue that our results for interferometers in the strong backscattering limit are related to an enhancement of shot noise observed experimentally in more open devices.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:74093 |
| Date | 05 March 2021 |
| Creators | Frigeri, Giovanni Andrea |
| Contributors | Universität Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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