  A projective symmetry group (PSG) has been regarded as a classification
theory of spin liquids. However, it does not include a symmetry-protected
topological order of fermionic spinon excitations, and thus the classification
of gapped spin liquids is incomplete. We demonstrate the classification beyond
PSG by utilizing the Kitaev model on the squareoctagon lattice, where two
gapped spin liquids are distinguished by a topological $Z_2$ invariant. This
$Z_2$ invariant can be defined solely by the time-reversal and translation
symmetries on condition that the time-reversal symmetry is implemented
projectively. Thus, it is a hidden class of topological Kitaev spin liquids
with helical edge states, which has been ignored for a long time. This suggests
that there exists an unknown classification scheme of gapped spin liquids
beyond PSG.
