The integer quantum Hall effect (IQHE) and chaos are commonly conceived as being unrelated. Contrary to common wisdoms, we find in a canonical chaotic system, the kicked spin-$1/2$ rotor, a Plancks quantum($h_e$)-driven phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically, the rotors energy growth is unbounded (metallic phase) for a discrete set of critical $h_e$-values, but otherwise bounded (insulating phase). The latter phase is topological in nature and characterized by a quantum number (quantized Hall conductance). The number jumps by unity whenever $h_e$ decreases passing through each critical value. Our findings, within the reach of cold-atom experiments, indicate that rich topological quantum phenomena may emerge from chaos.
Download