• spin-orbit interaction
• Rashba effect
• nanowire
• indium arsenide
• weak anti-localization

Over the past decades there has been a growing interest in the study of the spin-orbit interaction (SOI) in semiconductor systems motivated by the possibility of spintronics applications and quantum computing. SOI has been first discovered in the context of atomic physics as a relativistic correction coupling electron spin and momentum, but appears in similar fashion also in solid state systems.
Here, structures with strong spin-orbit coupling offer an ideal platform to develop circuits for the coherent manipulations of electron spins which has led to novel and efficient control schemes that can be applied to make spin transistors or spin-orbit qubits. Furthermore, SOI is one of the key ingredients for inducing exotic states of matter, such as topological superconductivity. In such systems, a semiconductor nanowire (NW) with strong spin-orbit coupling is proximized by a superconductor and is predicted to host Majorana zero modes when a Zeeman field is applied orthogonal to the spin-orbit vector. These modes, exhibiting a non-Abelian exchange statistics, may be used to encode topologically protected qubits.

Despite the vast interest and the variety of new exotic phenomena based on SOI, experimental evidences regarding its origin in semiconductor NWs and the vectorial dependence of the spin-orbit coupling are limited. Indeed, in quasi-1D systems, the electron properties are strongly affected by the surface states and the confinement potentials that depend on the nanowire geometry and position with respect to the underlying substrate. For instance, confinement can strongly enhance the electron gyromagnetic ratio and the contact between the nanowire and substrate is believed to induce an asymmetry in the confinement potential. In turn, this is the main source of the spin-orbit coupling acting via the Rashba effect and causes the pinning of the spin-orbit field in the plane of the substrate, as demonstrated for nanowire quantum dots and for Majorana nanowires.

In this thesis work, we take a different perspective and investigate the SOI in freely suspended nanowires which are not expected to display any intrinsic electrostatic asymmetry. In this way, we are able to reestablish the natural geometrical degeneracies since the suspended wires offer an ideal platform for studying the intrinsic SOI. The vectorial dependence of the SOI is investigated by tracking the weak anti-localization (WAL) peak in the magnetoconductance, while rotating the magnetic field orientation respect to the NW symmetry axes. WAL is a dampening of the weak localization (WL), i.e. the localization of charge due to constructive interference of electron waves along time-reversed paths, induced by the presence of SOI. While WL leads to a negative correction to the magnetoconductance, the WAL results in a positive one that depends on the electron spin relaxation. From the magnetic field dependence of these two competing effects, the relevant length scales over which spin and phase information are preserved, i.e. spin-orbit relaxation length and coherence length, can be extracted.
Studying the angular maps of the WAL signal, we demonstrate that the average SOI within the NW is isotropic and that our findings are consistent with a semiclassical 1D model of WAL. Moreover, by acting on properly designed side gates, we are able to apply an external electric field introducing an additional vectorial spin-orbit component whose strength can be controlled by external means.

Our findings show the WAL as practical tool to investigate the vectorial nature of the SOI and give important hints on its origin in suspended nanowires. The achieved vectorial control of the SOI can spark interests for spintronic applications and can inspire novel schemes for the manipulation of Majorana bound states.