  Localization due to disorder has been one of the most intriguing theoretical
concepts evolved in condensed matter. Here, we expand the theory of
localization by considering two types of disorder at the same time, namely the
original Anderson's disorder and the structural defect disorder, which has been
suggested to be a key component in recently discovered two-dimensional
amorphous materials. While increasing the degree of both disorders could induce
localization of wavefunction in real space, we find that a small degree of
structural defect disorder can significantly enhance the localization. As the
degree of structural defect disorder increases, localized states quickly appear
within the extended phase to enter a broad crossover region with mixed phases.
Full localization occurs when structural defect disorder reaches about 10
percent, even without considering the Anderson type disorder. Our theoretical
model provides a comprehensive understanding of localization in two-dimensional
amorphous materials and highlights the promising tunability of their transport
properties.
