Spin Hall and Edelstein effects in a ballistic quantum dot with Rashba spin-orbit coupling

We study spin-resolved transport in a ballistic quantum dot with Rashba spin-orbit coupling, focusing on charge-to-spin conversion and spin Hall effect. In the regime where the dot size is comparable to the Fermi wavelength, we identify a clear crossover from weak localization to weak antilocalization as the Rashba coupling increases. This transition is accompanied by gate-tunable spin currents of Edelstein and spin Hall type, whose behavior reflects the underlying electron wavefunction interference. Notably, the Edelstein current shows an inflection point at the critical Rashba strength, signaling the crossover from weak localization to weak antilocalization. In the presence of an in-plane magnetic field we also report a transition in angular periodicity of the magnetoresistance -- from $\pi$ to $2\pi$ -- arising from the interplay between spin-orbit interaction and Zeeman coupling. These results establish a direct link between quantum coherence, charge-to-spin conversion, and geometric confinement in mesoscopic systems.