  Excitonic insulator (EI) is an intriguing insulating phase of matter, where
electrons and holes are bonded into pairs, so called excitons, and form a
phase-coherent state via Bose-Einstein Condensation (BEC). Its theoretical
concept has been proposed several decades ago, but the followed research is
very limited, due to the rare occurrence of EI in natural materials and the
lack of manipulating method of excitonic condensation. In this paper, we report
the realization of a doping-controlled EI-to-semi-metal transition in
Ta$_2$NiSe$_5$ using $in$-$situ$ potassium deposition. Combining with
angle-resolved photoemission spectroscopy (ARPES), we delineate the evolution
of electronic structure through the EI transition with unprecedented precision.
The results not only show that Ta$ _2 $NiSe$ _5 $ (TNS) is an EI originated
from a semi-metal non-interacting band structure, but also resolve two
sequential transitions, which could be attributed to the phase-decoherence and
pair-breaking respectively. Our results unveil the Bardeen-Cooper-Schrieffer
(BCS)-BEC crossover behavior of TNS and demonstrate that its band structure and
excitonic binding energy can be tuned precisely via alkali-metal deposition.
This paves a way for investigations of BCS-BEC crossover phenomena, which could
provide insights into the many-body physics in condensed matters and other
many-body systems.
