<p dir="ltr">InSbAs is a promising platform for exploring topological superconductivity and spin-based device applications, thanks to its strong spin-orbit coupling (SOC) and high effective <i>g</i>-factor. This thesis investigates low-temperature transport of electrons confined in InSb_1-xAs_x quantum wells. Specifically, we study the properties of electrons confined in 2D and 0D by fabricating gated Hall bars and gate-defined quantum dots. Theoretical considerations suggest that InSbAs will have stronger SOC and a larger effective <i>g</i>-factor compared to InAs and InSb. Both the SOC and effective <i>g</i>-factor change as a function of arsenic mole fraction, but much remains to be understood in real material systems. Here, we study the dominant scattering mechanisms, effective mass, spin-orbit coupling strength, and the <i>g</i>-factor in InSb_1-xAs_x quantum wells grown by molecular beam epitaxy. </p><p dir="ltr">We explore 30 nm InSb_1-xAs_x quantum wells with arsenic mole fractions of <i>x</i> = 0.05, 0.13, and 0.19. The 2DEG properties were studied by fabricating gated Hall bars and placing them in a perpendicular magnetic field at low temperatures (T = 10 - 300 mK). All samples showed high-quality transport with mobility greater than 100,000 cm²/Vs. For the <i>x</i> = 0.05 sample, the 2DEG displays a peak mobility μ = 2.4 x 10⁵ cm²/Vs at a density of <i>n</i> = 2.5 x 10¹¹ cm^-². We investigated the evolution of mobility as a function of arsenic mole fraction and 2DEG density for all samples. As the arsenic mole fraction increases, peak mobility decreases, and the dependence of mobility on density becomes weaker, suggesting that short-range scattering becomes the dominant scattering mechanism. We extracted an alloy scattering rate of τ_alloy = 45 ns^-1 per % As, an important parameter for understanding the impact of disorder on induced superconductivity. The high mobility, strong spin-orbit coupling, and low effective mass in this material system resulted in a beating pattern in the Shubnikov de Haas oscillations, allowing for the extraction of the Rashba parameter as a function of density and arsenic mole fraction. We observed a gate tunable spin-orbit coupling and, as predicted by theory, an increase in spin-orbit coupling with increasing arsenic mole fraction. For the sample with x = 0.19, the highest Rashba parameter is α_R ~ 300 meVÅ, which is significantly higher than in InSb. </p><p dir="ltr">In addition, we explored 0D confinement by fabricating a gate-defined quantum dot in an InSb₀_.87As_0.13 quantum well. By studying the evolution of Coulomb blockade peaks and differential conductance peaks as a function of magnetic field, a nearly isotropic in-plane effective <i>g</i>-factor in the [1-10] and [110] crystallographic directions was extracted, ranging from 49-58. The values extracted are 1.8 times higher than in a quantum dot fabricated in pure InSb. Furthermore, this study produced the first demonstration of a tunable spin-orbit coupling in this material system. This was achieved by measuring the avoided crossing gap, mediated by spin-orbit coupling, between the ground state and excited state in a magnetic field. The avoided crossing gap indicates the strength of the spin-orbit coupling; the maximum energy separation extracted is Δ_SO ~100 μeV. </p><p dir="ltr">Our work should stimulate further investigation of InSbAs quantum wells as a promising platform for applications requiring strong spin-orbit coupling, such as topological superconductivity or spin-based devices.</p>

<p dir="ltr">The two-dimensional electron gas (2DEG) in shallow InAs quantum wells, combined with epitaxial aluminum, is commonly used to study topological superconductivity. Key features include strong spin-orbit coupling, a high effective g-factor, and the ability to manage proximity-induced superconductivity. My thesis discusses two aspects of this unique material. In the first section, I report on the transport characteristics of shallow InGaAs/InAs/InGaAs quantum wells and evaluate the effect of modulation doping on these shallow InAs quantum well structures. We systematically investigate the magnetotransport properties in relation to doping density and spacer thickness. Optimized samples show peak mobilities exceeding 100,000 cm²/Vs at n_2DEG < 10¹²cm^-2 in gated Hall bar, marking the highest mobility observed in this type of heterostructure. Our findings suggest that the doping layer moves the electron wave function away from the surface, minimizing surface scattering and enhancing mobility. This mobility improvement does not compromise Rashba spin-orbit coupling or induced superconductivity. In the second section, motivated by a theoretical study by Peng et al., we explore tunneling spectroscopy measurements on DC current biased planar Josephson junctions made on an undoped hybrid epitaxial Al-InAs 2DEG heterostructure. We observe four tunneling conductance peaks in the spectroscopy that can be adjusted by DC current bias. Our analysis indicates that these results come from strong coupling between the tunneling probe and the superconducting leads, rather than from Floquet engineering. We also touch on potential improvements to the device's design and materials. This work lays the groundwork for further investigation of Floquet physics in planar Josephson junctions. This thesis ends with a discussion of other unusual physics that could be explored in these novel shallow InAs quantum wells coupled with epitaxial aluminum.</p>