Quantum point contact with a large localized spin: Fractional quantization of the ballistic conductance

We analyze the conductance of the quantum point contact containing large localized spin $J$. The additional plateau is formed on a ballistic conductance staircase if only one propagating channel is rendered conducting. The conductance value at this plateau is shown to depend strongly on $J$ and decrease from $3{e}^{2}∕2h$ to ${e}^{2}∕h$ when $J$ increases from $\frac{1}{2}$ to infinity, which is in a good agreement with the experimental observations [D. J. Reilly et al., Phys. Rev. B 63, 121311 (2001)].