Anomalous spin transport in a two-channel-Kondo quantum dot device

We study the response of a two-channel Kondo quantum dot device proposed by Y. Oreg and D. Goldhaber-Gordon [Phys. Rev. Lett. {\bf 90}, 136602 (2003)] to a spin-bias applied across one of its channels formed by Fermi liquid reservoirs weakly coupled to a spin-1/2 quantum dot. When the temperature $T<T_K$, the Kondo temperature of the device, the spin conductance depends on the Kondo coupling of the dot spin to the other channel in an anomalous manner. For isotropic Kondo couplings to the two channels the spin conductance is quantized for $T\ll T_K$ characterizing the two-channel Kondo fixed point. On the other hand, for anisotropic couplings a crossover energy scale $T_A\neq 0$ determines the temperature $T\ll T_A$ when the spin conductance vanishes indicating one-channel Kondo behavior.