Universality of the Anderson Metal–Insulator Transition in 3D Lattices with Enhanced Connectivity

Building upon the foundational framework of Bloch theory and the disorder-induced breakdown of electronic delocalization, the phenomenon of Anderson localization continues to be a cornerstone in understanding transport suppression in disordered systems. While classical studies primarily focused on simple cubic or regular lattice geometries, recent investigations have shown that the underlying lattice topology and coordination number play pivotal roles in shaping the localization behavior and critical disorder threshold. In our work, we focus on Anderson localization in modified three-dimensional (3D) lattices, where structural modifications are introduced through an increase in coordination number and lattice connectivity.

Specifically, we explore 3D checkerboard lattices, 2D stacked checkerboard lattices, and 3D Lieb lattices, each offering distinct connectivity patterns and local geometrical variations compared to the conventional cubic framework. These structural alterations are expected to influence the degree of quantum interference and modify the mobility edge—the critical energy separating localized and extended states. By systematically tuning disorder strength and lattice topology, we aim to uncover how enhanced coordination and lattice complexity govern the transition between metallic and insulating regimes.

Using numerical simulations of tight-binding Hamiltonians, we analyze the scaling of the average level spacing ratio, inverse participation ratio, and density of states to characterize localization properties across different lattice types. Our numerical study provides new insights into how lattice modifications in higher dimensions can reshape the fundamental nature of Anderson localization.