  The impurities, introduced intentionally or accidentally into certain
materials, can significantly modify their characteristics or reveal their
intrinsic physical properties, and thus play an important role in solid-state
physics. Different from those static impurities in a solid, the impurities
realized in cold atomic systems are naturally mobile. Here we propose an
effective theory for treating some unique behaviors exhibited by ultracold
mobile impurities. Our theory reveals the interaction-induced transition
between the extended and localized impurity states, and also explains the
essential features obtained from several previous models in a unified way.
Based on our theory, we predict many intriguing phenomena in ultracold systems
associated with the extended and localized impurities, including the formation
of the impurity-molecules and impurity-lattices. We hope this investigation can
open up a new avenue for the future studies on ultracold mobile impurities.
