Anomalous amplitude mode dynamics below the expected charge-density-wave transition in 1$T$-VSe$_2$

A charge-density-wave (CDW) is characterized by a dynamical order parameter consisting of a time-dependent amplitude and phase, which manifest as optically-active collective modes of the CDW phase. Studying the behaviour of such collective modes in the time-domain, and their coupling with electronic and lattice order, provides important insight into the underlying mechanisms behind CDW formation. In this work, we report on femtosecond broadband transient reflectivity experiments on bulk 1$T$-VSe$_2$ using near-infrared excitation. At low temperature, we observe coherent oscillations associated with the CDW amplitude mode and phonons of the distorted lattice. Across the expected transition temperature at 110 K, we confirm signatures of a rearrangement of the electronic structure evident in the quasiparticle dynamics. However, we find that the amplitude mode instead softens to zero frequency at 80 K, possibly indicating an additional phase transition at this temperature. In addition, we demonstrate photoinduced CDW melting, associated with a collapse of the electronic and lattice order, which occurs at moderate excitation densities, consistent with a dominant electron-phonon CDW mechanism.