Spectrally resolving the phase and amplitude of coherent phonons in the charge density wave state of 1$T$-TaSe$_2$

Abstract: The excitation and detection of coherent phonons has given unique insights into condensed matter, in particular for materials with strong electron-phonon coupling. We report a study of coherent phonons in the layered charge density wave (CDW) compound 1$T$-TaSe$_2$ performed using transient broadband reflectivity spectroscopy, in the photon energy range 1.75-2.65 eV. Several intense and long lasting (> 20 ps) oscillations, arising from the CDW superlattice reconstruction, are observed allowing for detailed analysis of the spectral dependence of their amplitude and phase. We find that for energies above 2.4 eV, where transitions involve Ta d-bands, the CDW amplitude mode at 2.19 THz dominates the coherent response. At lower energies, instead, beating arises between additional frequencies, with a particularly intense mode at 2.95 THz. Interestingly, our spectral analysis reveals a $\pi$ phase shift at 2.4 eV. Results are discussed considering the selective coupling of specific modes to energy bands involved in the optical transitions seen in steady-state reflectivity. The work demonstrates how coherent phonon spectroscopy can distinguish and resolve optical states strongly coupled to the CDW order and provide additional information normally hidden in conventional steady-state experiments.