Classification of Collective Modes in a Charge Density Wave by Momentum-Dependent Modulation of the Electronic Band Structure

We present time- and angle-resolved photoemission spectroscopy measurements on the charge density wave system CeTe$_{3}$. Optical excitation transiently populates the unoccupied band structure and reveals a gap size of 2$Delta$ = 0.59 eV. The occupied Te-5p band dispersion is coherently modified by three modes at $Omega_{1}$ = 2.2 THz, $Omega_{2}$ = 2.7 THz and $Omega_{3}$ = 3 THz. All three modes lead to small rigid energy shifts whereas $Delta$ is only affected by $Omega_{1}$ and $Omega_{2}$. Their spatial polarization is analyzed by fits of a transient model dispersion and DFT frozen phonon calculations. We conclude that the modes $Omega_{1}$ and $Omega_{2}$ result from in-plane ionic lattice motions, which modulate the charge order, and that $Omega_{3}$ originates from a generic out-of-plane $A_{1g}$ phonon. We thereby demonstrate how the rich information from trARPES allows identification of collective modes and their spatial polarization, which explains the mode-dependent coupling to charge order.