  We derive the topological Kondo Hamiltonian describing a Y junction of three
  XX-spin chains connected to outer quantum Ising chains with different tilting
angles for the Ising axis. We show that the tilting angles in the spin models
play the role of the phases of the superconducting order parameters at the
interfaces between bulk superconductors and one-dimensional conducting normal
electronic wires. As a result, different tilting angles induce nonzero
equilibrium spin (super)currents through the junction.
  Employing the renormalization group approach to the topological Kondo model,
we derive the scaling formulas for the equilibrium spin currents. We argue
that, by monitoring the crossover in the currents induced by the Kondo effect,
it is possible to estimate the Kondo screening length. In particular, we prove
how it is possible to tune the Kondo length by acting on the applied phases
only; this enables us to map out the scaling properties by just tuning the
tilting angles and the Kondo length accordingly.
