Density invariant vibrational modes in disordered colloidal crystals

We experimentally measure the density of states (DOS) and dynamical structure factor (DSF) arising from the thermal fluctuations in a colloidal crystal composed of thermally sensitive micron-sized hydrogel particles at several different particle volume fractions, ϕ's. Particle positions are tracked over long times using optical microscopy and particle tracking algorithms in a single two-dimensional (2D) [111] plane of a 3D face-centered-cubic single crystal. The dynamical fluctuations are spatially heterogeneous while the lattice itself is highly ordered. At all ϕ's, the DOS exhibits an excess of low frequency modes, a so-called boson peak (BP), and the DSF exhibits a cross-over from propagating to nonpropagating behavior, a so-called Ioffe-Regel crossover, at a frequency somewhat below the BP for both longitudinal and transverse modes. As we tune ϕ from 0.64 to 0.56, the Lindemann parameter grows from ~3% to ~8%; however, the shape of the DOS and DSF remain largely unchanged when rescaled by the Debye level. This invariance indicates that the effective degree of disorder remains essentially constant even in the vicinity of melting.