  Two-dimensional (2D) topological materials (TMs) have attracted tremendous
attention due to the promise of revolutionary devices with non-dissipative
electric or spin currents. Unfortunately, the scarcity of 2D TMs holds back the
experimental realization of such devices. In this work, based on our recently
developed, highly efficient TM discovery algorithm using symmetry indicators,
we explore the possible 2D TMs in all non-magnetic compounds in four recently
proposed materials databases for possible 2D materials. We identify hundreds of
2D TM candidates, including 205 topological (crystalline) insulators and 299
topological semimetals. In particular, we highlight MoS, with a mirror Chern
number of -4, as a possible experimental platform for studying the
interaction-induced modification to the topological classification of
materials. Our results winnow out the topologically interesting 2D materials
from these databases and provide a TM gene pool which for further experimental
studies.
