The normal modes and the density of states (DOS) of any material provide a basis for understanding its thermal and mechanical transport properties. In perfect crystals, normal modes are plane waves, but they can be complex in disordered systems. We have experimentally measured normal modes and the DOS in a disordered colloidal crystal. The DOS shows Debye-like behavior at low energies and an excess of modes, or Boson peak, at higher energies. The normal modes take the form of plane waves hybridized with localized short wavelength features in the Debye regime but lose both longitudinal and transverse plane-wave character at a common energy near the Boson peak.

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 micronsized hydrogel particles at several different particle volume fractions, φ. 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, 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 non-propagating behavior, a so-called Ioffe-Regel (IR) 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.