Disorder‐Induced Transitions in Topological Phases of the Hofstadter Model

ABSTRACT Topological phases of matter are known for their robustness against perturbations, yet their stability under disorder remains an open question of both theoretical and experimental relevance. We study the disordered Hofstadter model, where magnetic flux generates fractal minibands carrying nontrivial Chern numbers. Using numerical simulations, we construct a disorder–flux phase diagram by computing Chern numbers and gap statistics across a wide range of parameters. We find that weak to moderate disorder preserves quantized Chern phases, while strong disorder closes mobility gaps, induces Chern‐number fluctuations, and drives transitions to trivial insulating states. Our results provide direct guidelines for engineering disorder and flux in synthetic lattices, with implications for quantum simulation and quantum device design.