  2D materials can host interesting physics and have important applications in
various fields. Recent experiment shows that monolayer PtSe$_2$ nanoflakes with
neutral zigzag edges are stable. Here, we study semiconducting PtSe$_2$
nanoribbons with the stable edges through first-principles investigation, and
find relativistic energy dispersion and large unconventional Rashba spin
splitting in the low-energy bands (even $N$) which originates from the
nanoribbon edges. Furthermore, there exists SU(2) spin symmetry in both of the
conduction and valence bands for each edge, which implies spin-conserving
carrier transport or persistent spin helix (in the spin xy plane). When the
inter-edge interaction becomes weak, a nearly-perfect Dirac fermion system can
be achieved through combining the valence and conduction bands. Thus we realize
unconventional Rashba splitting with double SU(2) spin symmetry and a pure
Dirac fermion system in condensed matter physics.
