Four-dimensional topological Anderson insulator with an emergent second Chern number

Four-dimensional (4D) topological insulators, which are impossible in real materials, have attracted much attention by virtue of the recent progress achieved in quantum simulations of higher-dimensional systems. In this paper, we employ the supercell approximation to investigate the disorder effects on a system that supports the 4D topological insulator phases characterized by quantized second Chern numbers and the normal insulator phase. We demonstrate that the 4D topological insulator phases are robust against weak disorders. Moreover, we reveal that disorder can transform a normal insulator to a 4D topological insulator with an emergent second Chern number, referred to as a 4D topological Anderson insulator. An effective-medium theory based on the Born approximation further confirms the numerical conclusions.