Coherent Phonon-Driven Band Renormalizations in 1T$'$-MoTe$_2$

Here, we investigate phonon mode- and electron band-selective electron-phonon couplings in centrosymmetric 1T$'$-MoTe$_2$ using time- and angle-resolved photoemission spectroscopy combined with frequency-domain analysis. Femtosecond near-infrared pulses excite coherent $A_g$-symmetric phonon modes at 2.34 THz, 3.34 THz, and 3.86 THz, which manifest as oscillatory modulations in photoemission intensity and binding energy across the valence bands. Pixel-wise Fourier analysis using recently developed methodologies reveals pronounced band selectivity with distinct coupling strengths for different electronic states and phonon modes, enabling the evaluation of band-renormalization amplitudes in the range of few meV. Ab initio calculations qualitatively reproduce the experimentally observed coupling patterns and relative trends, demonstrating the capability of combined experimental and theoretical approaches to resolve ultrafast electron-phonon interactions in quantum materials.