Chaotic electron diffusion through stochastic webs enhances current flow in superlattices

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic(1-22) as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmo-gorov-Arnold-Moser (KAM) theorem(1-3,6-9)-a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt(2). By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency(6-9). This type of dynamics has wide-ranging implications in the theory of plasma physics(10), tokamak fusion(11), turbulence(6,7,12), ion traps(13), and quasicrystals(6,8). Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice(22-27) with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns(6-10,12-16) in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.