  We investigate the edge magnetism and the spin transport properties of an
SU(2)-symmetric Kitaev spin liquid (KSL) model put forward by Yao and Lee
[Phys. Rev. Lett. \textbf{107}, 087205 (2011)] on the honeycomb lattice. In
this model, the spin degrees of freedom fractionalize into a $\mathbb{Z}_{2}$
static gauge field and three species of either gapless (Dirac) or gapped
(chiral) Majorana fermionic excitations. We find that, when a magnetic field is
applied to a zigzag edge, the Dirac KSL exhibits a nonlocal magnetization
associated with the existence of zero-energy edge modes. The application of a
spin bias $V=\mu_{\uparrow}-\mu_{\downarrow}$ at the interface of the spin
system with a normal metal produces a spin current into the KSL, which depends,
in the zero-temperature limit, as a power-law on $V$ for both Dirac and chiral
KSLs, but with different exponents. Lastly, we study the longitudinal spin
Seebeck effect, in which a spin current is driven by the combined action of a
magnetic field perpendicular to the plane of the honeycomb lattice and a
thermal gradient at the interface of the KSL with a metal. Our results suggest
that edge magnetization and spin transport can be used to probe the existence
of charge-neutral edge states in quantum spin liquids.
