Theory of negative differential conductivity in a superlattice miniband

Negative mobility, sliding, and delocalization for stochastic networks

We consider prototype configurations for quasi-one-dimensional stochastic networks that exhibit negative mobility, meaning that current decreases or even reversed as the bias is increased. We then explore the implications of disorder. In particular, we ask whether lower and upper bias thresholds restrict the possibility to witness nonzero current (sliding and antisliding transitions, respectively), and whether a delocalization effect manifests itself (crossover from over-damped to under-damped relaxation). In the latter context detailed analysis of the relaxation spectrum as a function of the bias is provided for both on-chain and off-chain disorder.

Multistability, chaos, and random signal generation in semiconductor superlattices

Historically, semiconductor superlattices, artificial periodic structures of different semiconductor materials, were invented with the purpose of engineering or manipulating the electronic properties of semiconductor devices. A key application lies in generating radiation sources, amplifiers, and detectors in the "unusual" spectral range of subterahertz and terahertz (0.1-10 THz), which cannot be readily realized using conventional radiation sources, the so-called THz gap. Efforts in the past three decades have demonstrated various nonlinear dynamical behaviors including chaos, suggesting the potential to exploit chaos in semiconductor superlattices as random signal sources (e.g., random number generators) in the THz frequency range. We consider a realistic model of hot electrons in semiconductor superlattice, taking into account the induced space charge field. Through a systematic exploration of the phase space we find that, when the system is subject to an external electrical driving of a single frequency, chaos is typically associated with the occurrence of multistability. That is, for a given parameter setting, while there are initial conditions that lead to chaotic trajectories, simultaneously there are other initial conditions that lead to regular motions. Transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt. Multistability thus presents an obstacle to utilizing the superlattice system as a reliable and robust random signal source. However, we demonstrate that, when an additional driving field of incommensurate frequency is applied, multistability can be eliminated, with chaos representing the only possible asymptotic behavior of the system. In such a case, a random initial condition will lead to a trajectory landing in a chaotic attractor with probability 1, making quasiperiodically driven semiconductor superlattices potentially as a reliable device for random signal generation to fill the THz gap. The interplay among noise, multistability, and chaos is also investigated.

Microscopic theory for negative differential mobility in crowded environments

We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of the obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Terahertz generation and chaotic dynamics in single-walled zigzag carbon nanotubes

We study self-sustained terahertz current oscillation and chaotic dynamics in semiconducting single-walled zigzag carbon nanotubes using the time-dependent drift diffusion equations. The current oscillation under a dc voltage bias originates from the negative differential velocity of carbon nanotube which induces the motion and recycling of unstable domain. Numerical simulation indicates that different nonlinear oscillatory modes appear when an external high-frequency ac voltage is superimposed to the dc voltage bias and its driving amplitude varies. The appearance of different nonlinear oscillating modes, including periodic and chaotic, is attributed to the competition between the natural oscillation and the external driving oscillation. The transitions between periodic and chaotic states are carefully studied using chaos-detecting methods, such as bifurcation diagram, phase portraits, first return map, and Fourier spectrum. The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitudes as the control parameter.

Nonlinear dc transport in graphene

Considering electron-impurity, electron-acoustic-phonon and electron-optical-phonon scatterings, the nonlinear steady-state transport properties of graphene are studied theoretically by means of the balance equation approach. We find that the conductivity as a function of electric field strength, E, exhibits strongly nonlinear behavior for E larger than a critical value, E(c)≈0.1 kV cm(-1). With the increase of E from zero, the conductivity first decreases slowly and then it falls rapidly when E>E(c). The dependence of electron temperature on E is also demonstrated.

Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures

We have theoretically investigated nonlinear free-carrier absorption of terahertz (THz) radiation in InAs/AlSb heterojunctions. By considering multiple photon process and conduction-valence interband impact ionization (II), we have determined the field and frequency dependent absorption rate. It is shown that (i). electron-disorder scatterings are important at low to intermediate field, and (ii). most importantly, the high field absorption is dominated by II processes. Our theory can satisfactorily explain a long-standing experimental result on the nonlinear absorption in the THz regime.

Statistical crossover characterization of the heterotic localized-extended transition

We investigated the spectral statistics of a quantum particle in a superlattice consisting of a disordered layer and a clean layer, possibly accompanied by random magnetic fields. Because a disordered layer has localized states and a clean layer has extended states, our quantum system shows a heterotic phase of an Anderson insulator and a normal metal. As the ratio of the volume of these two layers changes, the spectral statistics change from Poissonian to one of the Gaussian ensembles which characterize quantum chaos. A crossover distribution specified by two parameters is introduced to distinguish the transition from an integrable system to a quantum chaotic system during the heterotic phase from an Anderson transition in which the degree of random potentials is homogenous.

Wave fronts may move upstream in semiconductor superlattices

In weakly coupled, current biased, doped semiconductor superlattices, domain walls may move upstream against the flow of electrons. For appropriate doping values, a domain wall separating two electric-field domains moves downstream below a first critical current, it remains stationary between this value and a second critical current, and then moves upstream above. These conclusions are reached by using a comparison principle to analyze a discrete drift-diffusion model, and validated by numerical simulations. Possible experimental realizations are suggested.