During a band-gap-tuned semimetal-to-semiconductor transition, Coulomb
attraction between electrons and holes can cause spontaneously formed excitons
near the zero-band-gap point, or the Lifshitz transition point. This has become
an important route to realize bulk excitonic insulators -- an insulating ground
state distinct from single-particle band insulators. How this route manifests
from weak to strong coupling is not clear. In this work, using angle-resolved
photoemission spectroscopy (ARPES) and high-resolution synchrotron x-ray
diffraction (XRD), we investigate the broken symmetry state across the
semimetal-to-semiconductor transition in a leading bulk excitonic insulator
candidate system Ta2Ni(Se,S)5. A broken symmetry phase is found to be
continuously suppressed from the semimetal side to the semiconductor side,
contradicting the anticipated maximal excitonic instability around the Lifshitz
transition. Bolstered by first-principles and model calculations, we find
strong interband electron-phonon coupling to play a crucial role in the
enhanced symmetry breaking on the semimetal side of the phase diagram. Our
results not only provide insight into the longstanding debate of the nature of
intertwined orders in Ta2NiSe5, but also establish a basis for exploring
band-gap-tuned structural and electronic instabilities in strongly coupled
systems.Comment: 27 pages, 4 + 9 figure