D. Fowler

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 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 Kolmogorov–Arnold–Moser (KAM) theorem—a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, ‘non-KAM’ chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice 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 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.

Bifurcations and chaos in semiconductor superlattices with a tilted magnetic field

We study the effects of dissipation on electron transport in a semiconductor superlattice with an applied bias voltage and a magnetic field that is tilted relative to the superlattice axis. In previous work, we showed that, although the applied fields are stationary, they act like a terahertz plane wave, which strongly couples the Bloch and cyclotron motion of electrons within the lowest miniband. As a consequence, the electrons exhibit a unique type of Hamiltonian chaos, which creates an intricate mesh of conduction channels (a stochastic web) in phase space, leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling electrical resistance. In this paper, we investigate the effects of dissipation on the electron dynamics by modifying the semiclassical equations of motion to include a linear damping term. We demonstrate that, even in the presence of dissipation, deterministic chaos plays an important role in the electron transport process. We identify mechanisms for the onset of chaos and explore the associated sequence of bifurcations in the electron trajectories. When the Bloch and cyclotron frequencies are commensurate, complex multistability phenomena occur in the system. In particular, for fixed values of the control parameters several distinct stable regimes can coexist, each corresponding to different initial conditions. We show that this multistability has clear, experimentally observable, signatures in the electron transport characteristics.

Semiconductor charge transport driven by a picosecond strain pulse

We demonstrate that a picosecond strain pulse can be used to drive an electric current through both thin-film epilayer and heterostructure semiconductor crystals in the absence of an external electric field. By measuring the transient current pulses, we are able to clearly distinguish the effects of the coherent and incoherent components of the acoustic packet. The properties of the strain induced signal suggest a technique for exciting picosecond current pulses, which may be used to probe semiconductor devices.

Electron effective mass and mobility in heavily doped n-GaAsN probed by Raman scattering

We investigate inelastic light scattering by longitudinal optic phonon-plasmon coupled modes (LOPCMs) in a series of heavily Se-doped, n-type GaAs1−xNx epilayers with x<0.4%. We perform a line shape analysis of the LOPCM spectra to estimate the optical effective mass, mopt∗, and the scattering time of the conduction electrons in GaAsN. We use these results to evaluate an effective carrier mobility for our samples. The values thus obtained, which we compare with measured electron Hall mobilities, indicate that the x-dependence of the mobility in GaAs1−xNx is dominated by the scattering time, rather than by the variation of the electron effective mass. The Raman analysis yields mopt∗ values that are lower than those obtained from the band anticrossing model.

Using acoustic waves to induce high-frequency current oscillations in superlattices

We show that gigahertz acoustic waves in semiconductor superlattices can induce terahertz (THz) electron dynamics that depend critically on the wave amplitude. Below the threshold amplitude, the acoustic wave drags electrons through the superlattice with a peak drift velocity overshooting that produced by a static electric field. In this regime, single electrons perform drifting orbits with THz frequency components. When the wave amplitude exceeds the critical threshold, an abrupt onset of Bloch-type oscillations causes negative differential velocity. The acoustic wave also affects the collective behavior of the electrons by causing the formation of localized electron accumulation and depletion regions, which propagate through the superlattice, thereby producing self-sustained current oscillations even for very small wave amplitudes. We show that the underlying single-electron dynamics, in particular, the transition between the acoustic wave dragging and Bloch oscillation regimes, strongly influence the spatial distribution of the electrons and the form of the current oscillations. In particular, the amplitude of the current oscillations depends nonmonotonically on the strength of the acoustic wave, reflecting the variation in the single-electron drift velocity.

Current flow and energy dissipation in low-dimensional semiconductor superlattices

By applying high magnetic and electric fields to a semiconductor superlattice (SL) we create quasi-one-dimensional or quasi-zero-dimensional electronic states. This reduced dimensionality restricts the range of inelastic scattering processes available to the conduction electrons, leading to an increase of the inelastic scattering time and a corresponding decrease of the electrical conductance. Our study reveals the fundamental link between current flow and energy dissipation in low-dimensional conductors, which is relevant to the exploitation of artificial nanowires and quantum dot SLs for novel applications, including recently proposed thermoelectric devices.

Using sound to generate ultra-high-frequency electron dynamics in superlattices

We show that a phonon wave propagating through a semiconductor superlattice can induce a charge current even when no static electric field is applied. When the energy amplitude of the phonon wave is less than the width of the lowest superlattice miniband, we find strong resonant enhancement of electron transport, accompanied by very high frequency oscillations of the electron orbits. In this regime, the phonon wave drags the electrons through the superlattice, causing them to undergo quasi-periodic trajectories with a single dominant temporal frequency several orders of magnitude higher than that of the phonon deformation wave itself. This transformation of GHz frequency wave motion into highly coherent THz frequency electron dynamics provides a mechanism for frequency up-conversion, with a multiplication factor of ~20 in our present samples. For phonon wave amplitudes higher than the miniband width, the electrons perform Bloch-like oscillations, which dramatically suppresses transport.

Using Stochastic Webs to Control the Quantum Transport of Electrons in Semiconductor Superlattices

We show that electrons in a semiconductor superlattice can be used to realize and exploit the unique dynamics of the driven harmonic oscillator that were discovered and explored by George Zaslavsky and colleagues. Under the action of an electric and tilted magnetic field, the semiclassical dynamics of electrons in an energy band of the superlattice exhibit non-KAM chaos, which strongly affects the electrical conductivity. At certain critical field parameters, the electron trajectories change abruptly from fully localized to completely unbounded, and map out intricate stochastic webs in phase space, which act as conduction channels for the electrons. Delocalization of the electron paths produces a series of strong resonant peaks in the electron drift velocity versus electric field curves. We use these drift velocity characteristics to make self-consistent drift-diffusion calculations of the current-voltage and differential conductance-voltage curves of the superlattices, which agree well with our experimental data and reveal strong resonant features originating from the sudden delocalization of the stochastic single-electron paths. We show that this delocalization has a pronounced effect on the distribution of space charge and electric field domains within the superlattices. Inter-miniband tunneling greatly reduces the amount of space-charge buildup, thus enhancing the domain structure and both the strength and number of the current resonances.

Chaotic Transport in Semiconductor, Optical, and Cold-Atom Systems

We show that the reflection of quantum-mechanical waves from semiconductor surfaces creates new regimes of nonlinear dynamics, which offer sensitive control of electrons and ultra-cold atoms. For electrons in superlattices, comprising alternating layers of different semiconductor materials, multiple reflections of electron waves from the layer interfaces induce a unique type of chaotic electron motion when a bias voltage and tilted magnetic field are applied. Changing the field parameters switches the chaos on and off abruptly, thus producing a sharp increase in the measured current flow by creating unbounded electron orbits. These orbits correspond to either intricate web patterns or attractors in phase space depending on the electron decoherence rate. We show that related dynamics provide a mechanism for controlling the transmission of electromagnetic waves through spatially-modulated photonic crystals. Finally, we consider the quantum dynamics of a Bose-Einstein condensate, comprising 120,000 rubidium atoms cooled to 10 nK, incident on a stadium billiard etched in a room-temperature silicon surface. Despite the huge temperature difference between the condensate and the billiard, quantum-mechanical reflection can shield the cold atoms from the disruptive influence of the surface, thus enabling the billiard to imprint signatures of single-particle classical trajectories in the collective motion of the reflected atom cloud.

Raman scattering by LO phonon‐plasmon coupled modes in heavily doped Ga(AsN)

We use Raman scattering to investigate LO phonon‐plasmon coupled modes (LOPCMs) in a series of heavily doped n‐GaAs1−yNy samples with y in the 0.1–0.3% range. We find that the LOPCMs are highly damped in GaAs1−yNy, which is attributed to the disorder introduced by N. LOPCM lineshape calculations allow us to estimate the optical electron effective mass of GaAs1−yNy from the Raman spectra.