Bloch oscillations and other dynamical phenomena of electrons in semiconductor superlattices

We solve the time-dependent Schrödinger equation based on the complete Hamiltonian for independent electrons in ideal GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As superlattices, described by the conventional one-dimensional flat-band picture, subject to a uniform electric field F. Our approach consists of using high-accuracy numerical methods, thereby enabling us to avoid truncating the Hamiltonian or adopting other uncontrolled approximations. In suitable circumstances the electrons exhibit long-lived, time-periodic Bloch oscillations, in the form of either sinusoidal center-of-mass oscillations or a coherent breathing mode. Depending on the miniband structure of the superlattice, the value of F, and the form of the initial wave function, other dynamical phenomena can coexist with or even totally mask the Bloch oscillations. These are unbounded acceleration of a portion of the electron wave packet antiparallel to the electric field and intrawell oscillations. We provide the conditions under which each of these three basic dynamical elements occurs. We summarize the major results of our systematic investigation of the dependence of the electron dynamics on the entire parameter space of periodic potentials, field strengths, and initial wave functions.