Gate-tunable magnetic exchange and giant g-factor fluctuations in InAs nanowire quantum dots

We use the spin-1/2 Kondo effect, which is observed in every other charge ground state with odd elec-trons, to measure the field-induced splitting of the spin-doublet, and hence the $g$- factor. We do this in hybrid quantum dots using both normal (N), ferromagnetic (F) and superconducting (S) contacts. Unlike to previous studies, the $g$-factors of neighboring states can vary a lot: $g$ can scatter between $2$ and $18$ and can therefore be even larger than in the bulk ($g \sim 15$). We demonstrate further the electric gate tunability of the $g$- factor in a single charge state. When using F contacts, a zero- field split-ting is induced. This proximity induced exchange field has recently been measured for the first time by Hauptmann et al. (Nature Physics \textbf{4}, (2008)) in carbon nanotubes. Here, we show the same ef-fect in a semiconducting nanowire, demonstrating that this effect is universal. Employing a pair of S and F contacts, the proximity-induced exchange shows up as a minigap in superconducting spectroscopy.