Effects of magnetic field on electron transport in semiconductor superlattices

Quantum superlattice with a narrow energy band is an artificial semiconductor structure demonstrating both nonlinear and active high-frequency electromagnetic properties. These types of superlattices are used as key elements in various miniature electronic devices including frequency multipliers and quantum cascade lasers. Interaction between terahertz radiation and magnetic field in semiconductor superlattices has been the subject of growing research interest, both theoretical and experimental. In this thesis, we study the nonlinear dynamics of electrons in minibands of the semiconductor superlattices subjected to a terahertz electric field and a magnetic field. Electron transport in a semiconductor superlattice with an electric field and a tilted magnetic field has been studied using semiclassical equations. In particular, we consider how dynamics of electron in superlattices evolve with changing the strength and the tilt of a magnetic field. In order to investigate the influence of a tilted magnetic field on electron transport, we calculate the drift velocity for different values of the magnetic field. Studies have shown that the resonance of Bloch oscillations and cyclotron oscillations produces additional peaks in drift velocity. We also found out that appearance of these resonances can promote amplification of a small ac signal applied to the superlattice. In the presence of the electromagnetic field, the superlattice is expected to demonstrate the Hall effect, which however should have a number of very specific features due to an excitation of Bloch oscillations and a significant electric anisotropy. Here, we theoretically study the Hall effect in a semiconductor superlattice both for the steady electron transport and for the transient response. We studied the coherent Hall effect in an extraordinary configuration where the electric field is applied in the transverse direction of the superlattice growth direction. By mapping the momentum dynamics to the pendulum equivalent, we distinguished the two regimes of the oscillations from the viewpoint of the effective potentials. We discuss the experimental manifestation of the Hall effect in a realistic superlattice. We also made the numerical simulations of the polarized THz field and the time-resolved internal electro-optic sampling (TEOS) signals where we found the unusual shaped waveforms of the THz signals