The emergent correlation between unstable modes and superfast atoms in Cu50Zr50 glassy system

In recent work [Yang et al., Acta. Mater 281, 120410 (2024)], the rational structural representation of superfast “liquid-like” atoms in glasses was identified as ”cluster 3” via the unsupervised machine learning algorithm. Here, we further elucidate the connection of these superfast atoms to unstable instantaneous modes with imaginary frequencies (negative eigenvalues of the Hessian matrix), reflecting to transient saddle points on the potential energy landscape and thus potentially driving fast relaxations. Importantly, the localized unstable modes are characterized and found closely related to sub-picosecond lifetime. Moreover, the modified participation ratio ${\xi }_{\omega ,i}^{\mathrm{imag}}$ is proposed to specifically evaluate the contribution to unstable modes, revealing that cluster 3, i.e., superfast atoms shows significant coupling to unstable and localized modes, as evidenced by the remarkably high level of ${\xi }_{\omega ,i}^{\mathrm{imag}}$. This work establishes the emergent correlation among atomic structure, vibrational spectroscopy and relaxation phenomena in disordered materials.