  The cosmological applications of atomic clocks so far have been limited to
searches of the uniform-in-time drift of fundamental constants. In this paper,
we point out that a transient in time change of fundamental constants can be
induced by dark matter objects that have large spatial extent, and are built
from light non-Standard Model fields. The stability of this type of dark matter
can be dictated by the topological reasons. We point out that correlated
networks of atomic clocks, some of them already in existence, can be used as a
powerful tool to search for the topological defect dark matter, thus providing
another important fundamental physics application to the ever-improving
accuracy of atomic clocks. During the encounter with a topological defect, as
it sweeps through the network, initially synchronized clocks will become
desynchronized. Time discrepancies between spatially-separated clocks are
expected to exhibit a distinct signature, encoding defect's space structure and
its interaction strength with the Standard Model fields.
