Michal Piotr Nowak

We investigate the formation and transport properties of chiral Andreev edge states in a two-dimensional quantum Hall system proximitized by a superconductor. By numerically modeling the system using the Bogoliubov--de Gennes equations, we analyze the nonlocal conductance and transmission probabilities of multimode and spinful systems. We demonstrate that the Andreev reflection process induces a mixing of the quantum Hall edge modes at higher filling factors, a phenomenon strictly prohibited in clean, purely electronic systems. When incorporating the Zeeman interaction, we show that the Andreev edge states split into uncoupled spin species, maintaining spin orthogonality that prevents mixing between opposite spin sectors. Furthermore, we explore the impact of Rashba spin-orbit coupling. While the spin-orbit interaction alone causes slight spin depolarization, its combination with an in-plane magnetic field drives complex spin mixing among all chiral Andreev bands, fundamentally altering the conductance oscillations. Finally, we reveal that the electron transmission probabilities exhibit robust degeneracies, which emerge as a direct consequence of the unitarity constraints and the particle-hole symmetry of the system's scattering matrix in a magnetic field and the presence of spin-orbit interaction.

Multiple Andreev reflections in voltage-biased Josephson junctions give rise to the subharmonic gap structure in the conductance, which is widely used to characterize transport properties and estimate the induced gap in the junctions. Here we theoretically investigate the evolution of the subharmonic gap structure in spinful Josephson junctions. Spin mixing introduced by the spin-orbit coupling opens avoided crossings in the dispersion relation of the leads, which, as we demonstrate, subsequently results in pronounced multiple Andreev reflection features in the conductance traces. We analyze how these features evolve under an external magnetic field and explain that their visibility in conductance is governed by the spin polarization of the bands.

Multiple Andreev reflections in voltage-biased Josephson junctions give rise to the subharmonic gap structure in the conductance, which is widely used to characterize transport properties and estimate the induced gap in the junctions. Here we theoretically investigate the evolution of the subharmonic gap structure in spinful Josephson junctions. Spin mixing introduced by the spin-orbit coupling opens avoided crossings in the dispersion relation of the leads, which, as we demonstrate, subsequently results in pronounced multiple Andreev reflection features in the conductance traces. We analyze how these features evolve under an external magnetic field and explain that their visibility in conductance is governed by the spin polarization of the bands.

The hybrid system of a conventional superconductor (SC) on a semiconductor (SM) nanowire with strong spin-orbit coupling (SOC) represents a promising platform for achieving topological superconductivity and Majorana zero modes (MZMs) towards topological quantum computation. While aluminum (Al)-based hybrid nanowire devices have been widely utilized, their limited superconducting gap and intrinsic weak SOC as well as small Landé g-factor may hinder future experimental advancements. In contrast, we demonstrate that lead (Pb)-based hybrid quantum devices exhibit a remarkably large and hard proximity-induced superconducting gap, exceeding that of Al by an order of magnitude. By exploiting electrostatic gating to modulate wavefunction distribution and SC-SM interfacial coupling, this gap can be continuously tuned from its maximum value (~1.4 meV, matching the bulk Pb gap) down to nearly zero while maintaining the hardness. Furthermore, magnetic-field-dependent measurements reveal a radial evolution of the gap structure with anti-crossing feature, indicative of strong SOC and huge effective g-factors up to 76. These findings underscore the superior functionality of Pb-based hybrid systems, significantly advancing their potential for realizing and stabilizing MZMs and the further scalable topological quantum architectures.