Thesis Title: Bound states in hybrid superconductor-semiconductor nanowires: experimental analysis and theoretical proposals

Abstract: Fault-tolerant quantum computation demands many physical qubits per logical qubit, making scalability a central challenge. Topological quantum computation instead builds fault tolerance into the hardware using exotic quasiparticles such as Majorana zero modes (MZMs) that are topologically protected from local decoherence. A leading platform for MZMs is the quasi-1D hybrid superconductor-semiconductor nanowire. Realizing MZMs is fundamentally a materials engineering challenge, motivating a detailed understanding of the microscopic properties of these systems.

The experimental project in the thesis explores Sn-InAs nanowire Josephson junctions by studying Andreev bound states (ABS), which serve as direct probes of the junction’s defining properties. Sn is a strong alternative to conventional Al superconductor for its larger, hard-induced gap, expected to provide better protection against quasiparticle poisoning. This thesis presents, to our knowledge, the first ABS microwave spectroscopy measurements of Sn-based junctions.

Using circuit quantum electrodynamics (cQED) toolkit, we perform microwave spectroscopy on the junction embedded in an RF-SQUID and coupled to a coplanar-waveguide resonator. Two-tone spectroscopy maps the ABS dispersion versus flux and gate voltage, from which we estimate the mode transparency, induced gap, number of ABS modes, and their gate tunability. We resolve a unity-transparency mode that disperses towards zero energy at half flux, a trivial state resembling an MZM. We also observe signatures of spin-orbit splitting and multiple interacting ABS manifolds. Using single-tone spectroscopy, we analyze the junction’s current-phase-relation (CPR), skewness, harmonic content and critical current, and compare them with the Beenakker short-junction model.

Beyond the experiment, two theoretical proposals extend the platform from characterization to engineering functional devices. First, a single skewed ϕ0-junction can act as the nonlinear element of a three-wave-mixing parametric amplifier, providing an alternative to multi-junction SNAIL devices, using an applied magnetic field, or an on-chip micromagnet at zero field, to tune to the Kerr-free sweet spots dominated by the third-order nonlinearity. The second is motivated by the Sachdev-Ye-Kitaev model, where many MZMs interact via random, all-to-all four-body couplings. We propose an experimental realization of its smallest building block, a four-body MZM interaction, in a hybrid nanowire, and show how to detect and enhance this interaction through transport studies.