We find in a canonical chaotic system, the kicked spin-$1/2$ rotor, a Planck’s quantum($h_e$)-driven phenomenon bearing a close analogy to the integer quantum Hall effect but of chaos origin. Specifically, the rotor’s energy growth is unbounded (“metallic” phase) for a discrete set of critical values of $h_e$, but otherwise bounded (“insulating” phase). The latter phase is topological and characterized by a quantum number (“quantized Hall conductance”). The number jumps by unity whenever $h_e$ passes through each critical value as it decreases. Our findings indicate that rich topological quantum phenomena can emerge from chaos.

• Received 20 June 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.216802