Quantum Transport In Superlattices Research Articles

Stochastic webs and quantum transport in superlattices: an introductory review

Stochastic webs were discovered, first by Arnold for multi-dimensional Hamiltonian systems, and later by Chernikov et al. for the low-dimensional case. Generated by weak perturbations, they consist of thread-like regions of chaotic dynamics in phase space. Their importance is that, in principle, they enable transport from small energies to high energies. In this introductory review, we concentrate on low-dimensional stochastic webs and on their applications to quantum transport in semiconductor superlattices subject to electric and magnetic fields. We also describe a recently-suggested modification of the stochastic web to enhance chaotic transport through it and we discuss its possible applications to superlattices.

Regimes of quantum transport in superlattices in a weak magnetic field

Weak field magnetoresistance was explored in GaAs/AlGaAs superlattices withdifferent strengths of disorder produced either by the random variation of the wellthicknesses or by the interface roughness. Depending on the disorder strength, threedifferent regimes of the quantum transport were distinguished: the regimes ofweak localization identified as the regimes of propagative and diffusive Fermisurfaces and the strongly localized insulating regime. Our results imply differentdephasing mechanisms in the weak and strong localization limits. The verticalcoupling energies in the superlattices determined with the random variation of thewell thicknesses revealed a significant decrease with increasing disorder strength.

QUANTUM TRANSPORT IN SEMICONDUCTOR SUPERLATTICES BEYOND THE KADANOFF–BAYM ANSATZ

Quantum transport in semiconductor superlattices subject to quantizing parallel electric and magnetic fields is studied based on the Kadanoff–Baym–Keldysh double-time Green function approach. Exploiting the symmetry properties of the underlying Hamiltonian, coupled kinetic equations are derived and analytically solved for the density-of-states and the carrier distribution function. Scattering giving rise to collisional broadening plays an important role in our transport model, whose unperturbed eigenstates are completely discrete due to Wannier–Stark and Landau quantization. It is shown that a correct description of the stationary quantum transport in superlattices with field-induced localized eigenstates requires the determination of a time-dependent distribution function from a kinetic equation, which emerges beyond the Kadanoff–Baym Ansatz. Depending on the scattering strength, gaps are predicted to occur in the electric and magnetic field dependence of the current density. The rigorous quantum-mechanical approach reveals the hopping nature of the nonlinear transport in narrow miniband superlattices. This is compared with results obtained recently within the density-matrix approach.

Chaotic quantum transport in superlattices

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.

Inelastic Quantum Transport in Superlattices: Success and Failure of the Boltzmann Equation

Electrical transport in semiconductor superlattices is studied within a fully self-consistent quantum transport model based on nonequilibrium Green functions, including phonon and impurity scattering. We compute both the drift-velocity-field relation and the momentum distribution function covering the whole field range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport situation in the presence of inelastic scattering.

Combined description for semiclassical and quantum transport in superlattices

The dc current in strongly coupled superlattices can either be described in a semiclassical picture in terms of miniband transport or in a quantum mechanical theory based on hopping transitions between the localized wave functions of the Wannier-Stark ladder. We demonstrate the equivalence of both models in the field regime of Bloch-oscillating electrons. Combining these two pictures we calculate the superlattice drift velocity resulting from microscopic phonon scattering between the Wannier-Stark levels. Our results show that previous discussions of the temperature dependence of the drift velocity have to be revised drastically.