  Normal modes provide a fundamental basis for understanding crucial properties
of solids, such as the thermal conductivity, the heat capacity and the sound
propagation. While the normal modes are excellently described by plane waves in
crystals, they are far less understood in disordered systems, due to the great
difficulties in characterizing the heterogeneous vibrational behaviors. Using
charged colloids with long-range repulsion, we successfully make different
disordered systems without any contact friction, whose normal modes can be
visualized at single-particle level. In these systems, we directly tackle the
long-time outstanding puzzle in condensed matter physics: the microscopic
origin of the low-frequency modes in disordered systems. For the first time, we
experimentally clarify that the low-frequency modes are caused by the
collective resonance of relatively disordered particles (or soft structures)
coupled with long-wavelength transverse excitations, settling this puzzle at
single-particle level. Next to these low-frequency modes in the density of
states, we also observe a plateau due to isostaticity, verifying the
fundamental prediction of jamming model. Moreover, we reveal the intrinsic
correlation between the low-frequency modes and the real dynamics, which may
lead to a universal mechanism for aging, melting and yielding.

Soft Condensed Matter;Disordered Systems and Neural Networks;Materials Science