  $\alpha$-RuCl$_3$ is a promising candidate material for the Kitaev spin
liquid state where the half quantization of the thermal Hall effect, suggesting
a topological character, has been observed. However, its relation to the
existence of chiral Majorana fermions, which is predicted from the theory of
the Kitaev model, is still under debate. Here we propose a more direct
signature of a chiral Majorana edge mode which emerges in a universal scaling
of the Drude weight of the edge spin Seebeck effect in the Kitaev model.
Moreover, the absence of backscatterings in the chiral edge mode results in the
generation of a dissipationless spin current in spite of an extremely short
spin correlation length close to a lattice constant in the bulk. This result is
not only experimentally observable, but also opens a way towards spintronics
application of Kitaev materials. In contrast to magnetically ordered systems, a
Kitaev spin liquid state is stable even in the atomic scale and makes it
possible to fabricate a highly integrated device with substantial efficiency to
generate a spin current. This proposal for using $\alpha$-RuCl$_3$ as a
nano-scale device will pioneer Kitaev spintronics.
