Tunneling Spectroscopy of the Quantum Hall edge states using GaAs Quantum Wires

Edge states play a crucial role in many condensed matter systems, including the quantum Hall effect and topological insulators. Knowledge and control of the properties of the edge states is of particular importance for both fundamental understanding of novel materials and potential practical applications.
In this thesis a new spectroscopy technique to probe the integer quantum Hall edge states is demonstrated. For this, a GaAs cleaved edge overgrowth quantum wire is used as a momentum-conserving probe tunnel coupled to a 2D electron gas (2DEG), which at finite perpendicular magnetic field hosts the integer quantum Hall edge states. An in-plane magnetic field is used to match the momentum of the 1D wire with the momentum of an edge state, allowing one to discriminate spatially overlapping quantum Hall edge states. Using this technique, the momentum and the guiding center position of multiple integer quantum Hall edge states was tracked from very low magnetic fields all the way up to higher magnetic fields where individual edge states are magnetically depopulated. Analytical and numerical models that infer the properties of the edge states from the bulk spectrum were developed. These models quantitatively capture the whole magnetic field evolution of the observed tunneling resonances. Additionally, features that go beyond the single-particle picture such as exchange-enhanced spin splitting and signatures of edge-state reconstruction were also observed.
The ability to fabricate a 1D wires from other materials and tunnel couple them to novel systems, for example, topological insulators, would greatly broaden the applicability of the described spectroscopy technique. In addition, fabrication of the nanowires with strong spin-orbit interaction is also very important for the realization of the topological qubits based on Majorana Fermions, which are expected to be more robust against decoherence compared to the other types of qubits.
A promising growth technique of InGaAs nanowires on top of defect-free GaAs nanomembranes using molecular beam epitaxy was investigated. This growth technique is particularly attractive as it allows for the fabrication of patternable and highly regular branched nanowire arrays, necessary for scaling up the number of qubits. The coherence length of 130 nm and a lower bound on the spin-orbit length of 280 nm were obtained for such nanowires by fitting a simple quasi-1D transport model to magnetoconductance measurements.
The presence of quasiparticles in the superconductor could destroy the topological protection of the qubits based on Majorana fermions. The thermal population of quasiparticles also limits the operation temperature of the near term quantum computers based on superconducting qubits. For the normal metal-insulator-superconductor (NIS) tunnel junctions the quasiparticles produce a subgap leakage current characterized by the Dynes parameter.
By careful shielding and filtering of the measurement lines connected to the tunnel junction, finite-bias current steps were observed in the characteristic IV curves of NIS devices, which potentially could explain the origin of the phenomenological Dynes parameter. Qualitatively similar steps were observed in numerical simulations and were attributed to the sample specific geometry and disorder configuration enhanced Andreev reflections.