Superlattices Kinetic And Transport Theory

In this thesis, we investigate the dynamics and transport properties of electrons under the influence of electric fields, i.e., dynamics of coupled chains, dynamics of two-band superlattices, R.abi oscillations between Bloch bands in square-wave electric field, Dynamics of a single-band superlattice in a special electric field, and effect of external noise on the transport property.In chapter 2, we investigate the quasi-energy spectrum of a electon on coupled chains in the presence of both a uniform magnetic and an ac electric fields, and obtain the conditions of the dynamic localization (at one site or on one chain). The effect of magnetic field on the Rabi oscillations between the coupled chains is also discussed. We find that the uniform magnetic field can strongly affect the dynamic localization and the Rabi oscillations.In chapter 3, within a two-band tight-binding model driven by dc-ac electric fields, we investigate the dynamics of electrons between minibands. With the help of the Floquet theory, we obtain analytically the long-time averaged occupation probability P of an electron in either miniband. The miniband localization, Zener resonances and Rabi oscillations are all addressed quantificationally by the value of P. The effect of interband coupling on the dynamics is also discussed.In chapter 4, we investigate a tight-binding model of double Bloch bands driven by a square-wave electric field. By using Fourier analysis, we analytically obtain the resonance condition of Rabi oscillations and the Rabi frequency in the weak-coupling limit; and those results are verified by the numerical evolution results of electrons.In chapter 5. we investigate the dynamics of a superlattice with a single-band tight-binding model under a dc-trigonal wave electric field. we obtain analytically the conditions of the dynamical localization of the system: when the ratio of the Bloch frequency to electric field frequency is not, an integer, the system is always localized; when the ratio is an integer, the conditions of the localization depend on the Bloch frequency, the electric field frequency and the amplitude of the trigonal-wave electric field. The quasi-energy spectrums are also discussed, which show that the localization occurs at the collapse points of the quasi-energy band.In chapter 6, within a two-band tight-binding model driven by a dc-ac electric field, we investigate the effect of external noise on the transport property of electrons by controlling the strength and the decay constant of the noise. We find that external noise can destroy the periodicity of the transient current and cancel the long-time average current peaks. With increasing of the noise strength, the height of the current peaks will decrease, and the width will increase: a similar change will appear when we increase the decay constant of the noise.