Abstract

The quantum Hall (QH) effect is among the most remarkable and extensively studied phenomena in condensed matter physics. It has served as a platform for exploring a variety of exotic effects, such as the quantization of conductance arising from the formation of chiral edge channels. These edge channels remain central to both theoretical and experimental investigations of quantum Hall physics.

A significant fraction of quantum Hall experiments involves tunnelling contacts, known as quantum point contacts (QPCs), where quasiparticles can transfer between different edges. QPCs are essential tools for probing the physics of edge excitations, and they have enabled the experimental verification of predictions such as fractional quasiparticle charges. However, experiments with a single QPC often show discrepancies with theoretical predictions. While theory and experiment agree at small bias voltages, noticeable deviations appear at higher biases—specifically when the bias exceeds the system temperature but remains below the bulk energy gap. These discrepancies manifest both in the integer and, more prominently, in the fractional quantum Hall regimes.

In the first part of the project, we focus on addressing this discrepancy in the integer quantum Hall regime. One potential explanation is the energy dependence of the tunnelling amplitude, an effect absent in conventional models. In this work, we focus on the integer quantum Hall regime and introduce two models that account for the spatial extension of QPCs. The wide-QPC model incorporates the finite distance over which edges interact, while the long-QPC model considers the tunnelling amplitude arising from a finite bulk gap and separation between edges. Our analysis shows that these models predict opposite energy dependences of the tunnelling amplitude—either decreasing or increasing away from the Fermi level—highlighting the significant role of QPC geometry.

n the second part of the thesis, we investigate ultrafast pulses in interferometers in the terahertz regime. Electronic interferometers have been identified as potential platforms for realizing flying qubits, where pulses shorter than the device’s time of flight are required. Understanding the resulting dynamics necessitates accounting for electron-electron interactions. We perform time-resolved simulations of a Mach-Zehnder interferometer using a time-dependent mean-field treatment of interactions. Our results indicate that interactions primarily renormalize the pulse velocity, while the interference effects remain robust, demonstrating the resilience of quantum coherence under such conditions.

Although these two investigations address distinct systems, they collectively advance our understanding of quantum transport in mesoscopic systems. The insights gained here provide a foundation for the development of next-generation quantum devices and experimental protocols.