  Topological defects are singularities in the order parameter space that are
mathematically described by topological invariants and cannot be removed by
continuous transformations. These defects play a significant role in various
fields, ranging from cosmology to solid-state physics and biological matter.
The definition of these irregularities requires an ordered reference
configuration, leading to decades of debate about the existence of topological
defects in disordered systems, such as glasses. Recently, it has been proposed
that well-defined topological defects might emerge in the dynamical properties
of glasses under deformation, potentially relating to their plastic behavior.
In this study, we investigate a two-dimensional colloidal glass system composed
of particles interacting by an effective magnetic repulsion. We reveal the
presence of topological defects in the eigenspace of the vibrational
frequencies of this experimental 2D amorphous solid. The vibrational density of
states of this 2D amorphous material exhibits distinct glassy properties such
as the presence of a boson peak anomaly. Through extensive numerical and
theoretical quantitative analysis, we establish a robust positive correlation
between the vibrational characteristics and the total number of topological
defects. We furthermore show that defects of opposite charge tend to pair
together and prove their local statistical correlation with the "soft spots",
the regions more prone to plastic flow. This work provides the experimental
confirmation for the existence of topological defects in disordered systems
revealing a complex interplay between topology, disorder, and vibrational
behavior.
