  Recent discoveries of topological phases realized in electronic states in
solids have revealed an important role of topology, which ubiquitously appears
in various materials in nature. Many well-known materials have turned out to be
topological materials, and this new viewpoint of topology has opened a new
horizon in material science. In this paper we find that electrides are suitable
for achieving various topological phases, including topological insulating and
topological semimetal phases. In the electrides, in which electrons serve as
anions, the bands occupied by the anionic electrons lie near the Fermi level,
because the anionic electrons are weakly bound by the lattice. This property of
the electrides is favorable for achieving band inversions needed for
topological phases, and thus the electrides are prone to topological phases.
From such a point of view, we find many topological electrides, Y$_2$C
(nodal-line semimetal (NLS)), Sc$_2$C (insulator with $\pi$ Zak phase),
Sr$_2$Bi (NLS), HfBr (quantum spin Hall system), and LaBr (quantum anomalous
Hall insulator), by using ab initio calculation. The close relationship between
the electrides and the topological materials is useful in material science in
both fields.
