Chaotic quantum transport in superlattices

Abstract

We report a new type of quantum chaotic system inwhich the classical Hamiltonian originates from the intrinsically quantum mechanical nature of the device. The system is asemiconductor superlattice in a magnetic field. The energy–momentum dispersion curves can be used to calculate semi-classical orbits for electrons confined to a single miniband.When a magnetic field is applied along the superlattice axis(x-direction), the electrons perform Bloch oscillations along theaxis with cyclotron motion in the orthogonal plane. But whenthe magnetic field is tilted away from the x-direction, the orbitsare chaotic, and have a spatial width along the superlattice axis,which is much larger than the amplitude of the Blochoscillations. This is because the tilted field transfers momentum between the x- and z-directions, thereby delocalizing theelectron path. This type of chaotic dynamics is fundamentallydifferent to that identified in our previous studies of double–barrier resonant tunneling diodes. We investigate the relationbetween the orbits of the effective Hamiltonian, and thequantum states of the superlattice. In the regime of strongchaos, the wave functions have a highly diffuse structure whichextends across many periods of the superlattice, just like thecorresponding classical orbits. This chaos-induced delocalization increases the current flow through real devices. Bycontrast, in the stable domain the electron orbits remainlocalized along the paths of particular quasi-periodic orbits.We use theoretical and experimental current–voltage curves toshow how the onset of chaos manifests itself in the transportproperties of two- and three-terminal superlattice structures,and identify current oscillations associated with classicalresonances. We also consider analogies with ultra-cold atomsin an optical lattice with a tilted harmonic trap.