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The Wigner-Moyal approach is applied to investigate the dynamics of the Gaussian wave packet moving in a double-well potential in the ‘Mexican hat’ form. Quantum trajectories in the phase space are computed for different kinetic energies of the initial wave packet in the Wigner form. The results are compared with the classical trajectories. Some additional information on the dynamics of the wave packet in the phase space is extracted from the analysis of the cross-correlation of the Wigner distribution function with itself at different points in time.

The influence of the applied gate voltage on the coherent propagation of the conduction electrons through the InGaAs/InP core-multishell nanowires with the surrounding gate is considered. The solution of the threedimensional Schrodinger equation within the eective mass approximation is found using the adiabatic method. The electrostatic potential distribution generated by the all-around gate is determined from the self-consistent procedure applied to the Schrodinger‐Poisson problem. The Landauer‐Buttiker formalism and quantum transmission boundary method are applied to calculate the transport properties of the considered nanosystem.

The non-classical distribution function formalism is used for studying the electron transport in a nanosystem. We calculated the current–voltage characteristics of a triple barrier one-dimensional nanostructure which is connected to three-dimensional (highly doped semiconductor) reservoirs by the ohmic contacts. We also estimated the peak-to-valley ratio for the considered nanostructure and discussed the effect of switching the bias from peak-to-valley and from valley-to-peak voltages.

The spin-dependent electronic transport is investigated in a paramagnetic resonant tunnelling diode formed from Zn1−xMnxSe quantum well between two ZnBeSe barrier layers. The spin-dependent current–voltage characteristics have been obtained in the presence of magnetic fields by solving the quantum kinetic equation for the Wigner distribution function and the Poisson equation in the self-consistent procedure. We have obtained two distinct current peaks due to the giant Zeeman splitting of electronic levels in a qualitative agreement with experiment. We have shown that the sign of spin current polarization can be reversed by tuning the bias voltage. Moreover, we have found the bias voltage windows with a nearly constant polarization.

The theory of electron transport in disordered media such as liquid metals and amorphous alloys has been considerably developed since the fundamental papers by Ziman [1] and Faber and Ziman [2]. A very good review of the present knowledge m this field was given in the paper of Howson and Gallagher [3]. It is clear that the main contribution to the electrical resistivity in these materials comes from the elastic scattering of conduction electrons from a random array of potentials. There are some other mechanisms which can change this simple picture. One of them is the spin-orbit scattering which is to be discussed in this paper. It is important to take into account this contribution because it always exists and becomes significant in materials containing elements with higher atomic number Z. Many authors consider the inverse spin-orbit relaxation time τSO-1 which measures the strength of the spin-orbit coupling but they introduce τ in a phenomenological way and estimate its value by fitting the theoretical formulae to the experimental curves for the resistivity or conductivity (see e.g. [4-7]). However, the modification of the inverse relaxation time 7.-1 due to the spin-orbit scattering can be calculated from the quantum theory of scattering.

A theoretical description is given for electronic properties of semicon- ductor quantum dots in a magnetic field. A two-electron model is applied for electrons in a cylindrical quantum dot with a parabolic confinement po- tential. The eigenvalue problem is solved by the variational method with the trial wave function proposed in the form of linear combination of S-type and P-type Gaussians. The energy levels of singlet and triplet states with arbitrary radial and magnetic quantum numbers have been calculated as a function of the applied magnetic field. The calculated cyclotron transition energies agree well with those measured for InGaAs/GaAs quantum dots. It is shown that the electron-electron interaction has a small influence on the transition energy.

The modification of the electronic current resulting from Stark resonances has been studied for the semiconductor nanowire with the double-barrier structure. Based on the calculated current-voltage characteristics we have shown that the resonant tunneling current is a periodic function of the width of the spacer layer. We have also demonstrated that the simultaneous change of the source-drain voltage and the voltage applied to the gate located near the nanowire leads to almost periodic changes of the resonant tunneling current as a function of the source-drain and gate voltages. The periodic properties of the resonant tunneling current result from the formation of the Stark resonance states. If we change the electric field acting in the nanowire, the Stark states periodically acquire the energies from the transport window and enhance the tunneling current in a periodic manner. We have found that the separations between the resonant current peaks on the source-drain voltage scale can be described by a slowly increasing linear function of the Stark state quantum number. This allows us to identify the quantum states that are responsible for the enhancement of the resonant tunneling. We have proposed a method of the experimental observation of the Stark resonances in semiconductor double-barrier heterostructures., 9 pages, 8 figures

We have studied the spin splitting of the current in the Y-shaped semiconductor nanostructure with a quantum point contact (QPC) in a perpendicular magnetic field. Our calculations show that the appropriate tuning of the QPC potential and the external magnetic field leads to an almost perfect separation of the spin-polarized currents: electrons with opposite spins flow out through different output branches. The spin splitting results from the joint effect of the QPC, the spin Zeeman splitting, and the electron transport through the edge states formed in the nanowire at the sufficiently high magnetic field. The Y-shaped nanostructure can be used to split the unpolarized current into two spin currents with opposite spins as well as to detect the flow of the spin current. We have found that the separation of the spin currents is only slightly affected by the Rashba spin-orbit coupling. The spin-splitter device is an analogue of the optical device—the birefractive crystal that splits the unpolarized light into two beams with perpendicular polarizations. In the magnetic-field range, in which the current is carried through the edges states, the spin splitting is robust against the spin-independent scattering. This feature opens up a possibility of the application of the Y-shaped nanostructure as a non-ballistic spin-splitter device in spintronics.

Intrinsic terahertz oscillations of the electronic current in the asymmetric triple-barrier resonant tunneling diode are investigated by means of the time-dependent Wigner-Poisson method. The current-voltage characteristics calculated for the nanodevice exhibits four separate bias voltage windows with the current oscillations, which are caused by two different mechanisms. One of these bias voltage windows, for which the electronic current oscillations stem from the negative feedback between the electronic current and the coupled quasi-bound states in the quantum wells embedded in the active region of the nanodevice, is considered in detail. It is demonstrated that the amplitude and frequency of the current oscillations in this bias voltage window depend on the coupling between the quasi-bound states formed in the quantum wells. Strength of this coupling is controlled by the thickness of the central barrier separating the quantum wells, which allows to tune the amplitude and frequency of the terahertz oscillations. Additionally, it was shown that the amplitude of the current oscillations can be tuned by shifting up or down the energy of the bottom of the wider quantum well. These properties suggest that the considered nanodevice may be of interest because of its possible application as tunable terahertz generator.

The problem of spin-dependent transport of electrons through a metallic nanostructure is considered. The system consists of non-magnetic metal wire with two magnetic impurities and is connected to two ferromagnetic leads. The differential conductance is calculated by using the transfer matrix method. The spin polarization of the conductance is also obtained. It was found that this polarization is dependent on the spin configuration of magnetic impurities. This dependence can be controlled by the applied bias voltage.

Calculations of the quantum correction to the DC conductance of a cylindrical nanowire due to the quantum interference are presented. The real space Cooperon equation is solved for cylindrical geometry. Using this approach, it is shown that the quantum correction to the conductance in the weak localisation regime depends not only on the dephasing processes but also on geometrical parameters of the nanowire.