  A discrete time crystal is a phase unique to nonequilibrium systems, where
discrete time translation symmetry is spontaneously broken. Most of
conventional time crystals proposed so far rely on spontaneous breaking of
on-site symmetries and their corresponding on-site symmetry operations. In this
Letter, we propose a new time crystal dubbed "spatial-translation-induced
discrete time crystal (STI-DTC)", which is realized by spatial translation and
its symmetry breaking. Owing to the properties of spatial translation, in this
new time crystal, various time crystal orders can emerge only by changing the
filling but not changing the driving protocol. We demonstrate that local
transport of charges or spins shows a nontrivial oscillation, enabling
detection and applications of time crystal orders. Our proposal opens up a new
avenue of realizing time crystal orders by spatial translation.
