Photo-induced phase transitions have been intensively studied owing to the ability to control a material of interest in the ultrafast manner, which can induce exotic phases unable to be attained at equilibrium. However, the key mechanisms are still under debate, and it has currently been a central issue how the couplings between the electron, lattice, and spin degrees of freedom are evolving during photo-induced phase transitions. Here, we develop a new analysis method, frequency-domain angle-resolved photoemission spectroscopy, to gain precise insight into electron-phonon couplings during photo-induced insulator-to-metal transitions for Ta$_2$NiSe$_5$. We demonstrate that multiple coherent phonons generated by displacive excitations show band-selective coupling to the electrons. Furthermore, we find that the lattice modulation corresponding to the 2 THz phonon mode, where Ta lattice is sheared along the a-axis, is the most relevant for the photo-induced semimetallic state.
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