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<p dir="ltr">Improvement in state-of-the-art molecular beam epitaxy has led to the growth of ultra-high-quality GaAs/AlGaAs heterostructures. Two-dimensional electron systems in GaAs/AlGaAs heterostructures have provided a platform for investigating numerous phenomena in condensed matter physics.</p><p dir="ltr">In Chapter 2, we study low-frequency charge noise in shallow GaAs/AlGaAs heterostructures using quantum point contacts as charge sensors. We observe that devices with an Al$_2$O$_33$ dielectric between the metal gates and semiconductor exhibit significantly lower charge noise than devices with only Schottky gates and no dielectric. The improvement in device stability allows the application of shallow structures for spin qubit projects, making gate potential sharply defined.</p><p dir="ltr">In Chapter 3, we investigated the impact of edge-edge interaction on an electronic Fabry-P\'erot interferometer in the quantum Hall regime. Recently, experimental observations of periodicity $\phi_0/2$ in the integer</p><p dir="ltr">quantum Hall regime has been attributed to an exotic electron pairing mechanism. We present measurements of a Fabry-P\'erot interferometer operated in the integer quantum Hall regime at filling factor $1\leq \nu \leq 3$. Like previous experimental reports, under specific conditions we observe oscillations with flux periodicity $\phi_{0}/2$. However, our data and analysis indicate that period-halving is not driven by electron pairing, as has previously been claimed in the literature, but rather, is the result of electrostatic coupling between multiple independent edge modes.</p><p dir="ltr">In Chapter 4, we demonstrated our attempts in realizing stable {\it in-situ} gating for probing the possible non-Abelian state $\nu=5/2$. Utilizing a trench gate technique on a doped AlGaAs sample exhibits reasonable gating in a standard experiment time scale. Introducing AlAs screening wells further enhances the stability; it also significantly improves the coherence of interference at both integer and fractional states. In the future work section, we propose possible heterostructure modifications to improve contact performance, 2DEG quality, and the coherence of the interference.</p>