Spin precession in spin-orbit coupled weak links: Coulomb repulsion and Pauli quenching

A simple model for the transmission of pairs of electrons through a weak electric link in the form of a nanowire made of a material with strong electron spin-orbit interaction (SOI) is presented, with emphasis on the effects of Coulomb interactions and the Pauli exclusion principle. The constraints due to the Pauli principle are shown to “quench” the coherent SOI-induced precession of the spins when the spatial wave packets of the two electrons overlap significantly. The quenching, which results from the projection of the pair's spin states onto spin-up and spin-down states on the link, breaks up the coherent propagation in the link into a sequence of coherent hops that add incoherently. Applying the model to the transmission of Cooper pairs between two superconductors, we find that in spite of Pauli quenching, the Josephson current oscillates with the strength of the SOI, but may even change its sign (compared to the limit of the Coulomb blockade, when the quenching is absent). Conditions for an experimental detection of these features are discussed.

Figure 1

The average Josephson current $\overline{j}$ vs $2k_{\mathrm{so}}d/\pi$, for various values of the Coulomb repulsion, as encoded in $Z$: $Z=0$ (solid line) and $Z=0.2,0.4$ (increasing dashes). Inset: A narrower range, where $\overline{j}$ changes sign.