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Abstract
The fractional quantum Hall effect occurs when an extremely clean 2-dimensional fermion gas is subject to a magnetic field. This simple set of circumstances creates phenomena, such as edge reconstruction and fractional statistics, that remain subjects of experimental study 30 years after the discovery of the fractional quantum Hall effect. This thesis investigates the properties of excitations of the fractional quantum Hall effect.
The first set of experiments studies the interaction between fractional quantum Hall quasiparticles and nuclei in a quantum point contact (QPC). Following the application of a DC bias, fractional plateaus in the QPC shift symmetrically about half filling of the lowest Landau level, ν = 1/3, suggesting an interpretation in terms of composite fermions. Mapping the effects from the integer to fractional regimes extends the composite fermion picture to include hyperfine coupling.
The second set of experiments studies the tunneling of quasiparticles through an antidot in the integer and fractional quantum Hall effect. In the integer regime, we conclude that oscillations are of the Coulomb type from the scaling of magnetic field period with the number of edges bound to the antidot. Generalizing this picture to the fractional regime, we find (based on magnetic field and gate-voltage periods) at ν = 2/3 a tunneling charge of (2/3)e and a single charged edge. Further unpublished data related to this experiment as well as alternative theoretical explanations are also presented.
The third set of experiments investigates the properties of the fractional quantum Hall effect in the lowest Landau level of bilayer graphene using a scanning single-electron transistor. We observe a sequence of states which breaks particle-hole symmetry and instead obeys a ν → ν + 2 symmetry. This asymmetry highlights the importance of the orbital degeneracy for many-body states in bilayer graphene.
The fourth set of experiments investigates the coupling between microwaves and the fractional quantum Hall effect. Reflectometry is used to investigate bulk properties of samples with different electron densities. We observe large changes in the amplitude of the reflected signal at each integer filling factor as well as changes in the capacitance of the system.