Theoretical Studies Of Condensed Matter In A Number Of Nonlinear Phenomena

Bloch oscillation has been predicted long ago. In 1969, L. Esaki and R.Tsu proposed the superlattice that would facilitate the observation of quantum mechanical properties of Bloch states in a new domain of physical scale. The narrow energy bands of superlattice make it possible for electrons to be accelerated beyond the inflection point with moderate electric fields, leading to NDC and maybe leading to localized Bloch oscillation.The transport properties of superlattices have been studied by many authors experimentally and theoretically, and the theoretical studies of NDC are mainly done by the Boltzmann equation.We analyse the transport properties by the Fokker-Planck equation (FPE), and obtain some new results. We give an analysis of the perpendicular Bloch transport of electrons in a superlattice miniband for both the steady state and the oscillation cases. We have calculated the averaged drift -velocity in a superlattice. When the momentum relaxation time τ is fixed, the steady-state drift-velocity/uniform-field characteristics exhibit the expected maximum followed by negative differential conductivity (NDC). The onset field strength for the NDC is in agreement with the experiment. When the field is large, we have obtained the relation of velocity-oscillation, and its frequency is a increasing function of the field strength. Particularly, we give a new result about the oscillation frequency as a function of momentum relaxation time t, and, as expected, the frequency is the Bloch frequency Ω when τ become infinite.The Wannier-Stark ladders are the energy spectrum of superlattice electron under a steady electric field, and the Bloch oscillation is its characteristic of motion in the real space. The relation between Wannier-Stark ladders and Bloch oscillation is discussed by Green function. They are two related properties of superlattice electrons under a steady electric field.It is well known that application of sufficiently high drift fields to n-type GaAs and a number of other compound semiconductors can give rise to a far-from-equilibrium...