Doping-controlled transition from excitonic insulator to semimetal in Ta$_2$NiSe$_5$

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.