Phase fluctuation dynamics across the disordered charge density wave transition of Cu intercalated TiSe₂

Equilibrium fluctuations exhibit a diverging correlation length and correlation time near the transition temperature of a critical phase transition. In the presence of quenched disorder, these fluctuations are considerably altered; this additionally impacts the properties of the ordered state instigating a crossover from long-range to short-range order. Here, we employ x-ray photon correlation spectroscopy to study the phase transition of the 2 x 2 x 2 CDW in 8% Cu intercalated TiSe₂. This measurement technique provides information on the long time scale (~ 1 s) dynamics of the CDW texture over length scales on the order of 100 nm. The phase transition in this disordered system is spatially heterogeneous and smeared over a range of temperatures. Above the nominal Tc, nm scale islands of short-range order form in rare regions. The CDW phase in these regions is uncorrelated and fluctuates due to thermal activation on minute time scales. As the temperature is decreased, these ordered islands grow and become phase coherent resulting in an exponential increase in the correlation time. These results provide a time-resolved view on the phase transition process in a disordered CDW system.