  In a topological insulator, it is the electrons on the surface or edge that
carry the signature of topology. Recently, a novel topological state has been
proposed in metals or semimetals (gapless) whose band-structure is similar to
that of a three-dimensional analog of graphene. However, to this date the
signature of its topology remains an open question. We report the experimental
discovery of a pair of polarized Fermi arc surface state modes in the form of a
new type of two-dimensional polarized electron gas on the surfaces of Dirac
semimetals. These Fermi arc surface states (FASS) are observed to connect
across an even number of bulk band gapless nodes and found to have their spin
uniquely locked to their momentum. We show that these states are distinctly
different from the topological surface states (TSS) seen in all known
topological insulators. Our observed exotic two-dimensional states not only
uncover the novel topology of gapless Dirac metals (such as sodium tribismuth
Na$_3$Bi) but also opens new research frontiers for the utilization of
topological Fermi arc electron gases for a wide range of fundamental physics
and spintronic studies.
