Dynamics of Charge-Density-Wave puddles in 2$H$-NbSe$_2$
Electronic phases in quantum materials are often governed by nanoscale inhomogeneity, where local order develops within spatially confined regions or puddles. A prominent example is an incommensurate charge-density-wave (I-CDW) that comprises locally commensurate domains. In 2$H$-NbSe$_2$, such an I-CDW state persists alongside lattice anharmonicity and superconductivity, raising fundamental questions about the dynamical stabilization of CDW order in puddles. Here, we probe the puddle-dynamics in 2$H$-NbSe$_2$. Raman scattering reveals a strong Fano-coupling between the interlayer shear vibration and the CDW amplitude mode. Time-resolved reflectivity measurement shows a low-frequency ~0.15 THz coherent overdamped oscillation onsetting within the CDW regime at ~17 K, pointing towards a so far unexplored transition. This we identify as a Fano-coupled phonon-CDW hybrid emerging from the collective dynamics of CDW puddles. We establish a framework for capturing intertwinned glassy dynamics with an overdamped oscillatory model. Such dynamics in 2H-NbSe2 highlight how lattice pinning and electronic correlations in layered materials affect the CDW order, which is crucial for the design of novel Van der Waals devices.