Order parameter for structural heterogeneity in disordered solids.

We construct a structural order parameter from the energy equipartition of normal modes of vibration to quantify the structural heterogeneity in disordered solids. The order parameter exhibits strong spatial correlations with low-temperature dynamics and local structural entropy. To characterize the role of particles with the most defective local structures identified by the order parameter, we pin them and measure the system response. It turns out that particles with the largest value of the order parameter are responsible for the quasilocalized low-frequency vibration, instability, softening, and nonaffinity of disordered solids. The order parameter thus crucially links the heterogeneous structure to low-temperature dynamics and mechanical properties of disordered solids.