Conectividade da paisagem de localização em sistemas desordenados

Abstract

In this work, we investigate, within the framework of percolation theory, how disorder introduced by a binary potential affects the connectivity of the localization landscape in twodimensional systems. This analysis is particularly relevant because the localization landscape provides a geometric interpretation of electronic confinement and transport conditions in disordered media. The landscape is obtained by solving the linear system associated with the discretized Hamiltonian of the system. We then introduce a threshold parameter that allows the identification of connected regions and the characterization of cluster formation within the landscape. Using this approach, we determine the critical connectivity threshold associated with the geometric transition of the system. Our results show that reducing the disorder strength promotes the formation of percolating paths, decreases landscape fragmentation, and shifts the critical threshold to lower values. These findings reveal a direct connection between the structure of the localization landscape and the geometric connectivity properties induced by disorder, providing a novel perspective on the interplay between disorder, localization, and percolation phenomena.