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The purpose of this study is to apply the distribution function formalism to the problem of electronic transport in open systems, and to numerically solve the kinetic equation with a dissipation term. This term is modeled within the relaxation time approximation and contains two parts, corresponding to elastic or inelastic processes. The collision operator is approximated as a sum of the semi-classical energy dissipation term and the momentum relaxation term, which randomizes the momentum but does not change the energy. As a result, the distribution of charge carriers changes due to the dissipation processes, which has a profound impact on the electronic transport through the simulated region discussed in terms of the current–voltage characteristics and their modification caused by the scattering. Measurements of the current–voltage characteristics for titanium dioxide thin layers are also presented, and compared with the results of numerical calculations.

Using the phase space approach, we consider the quantum dynamics of a wave packet in an isolated confined system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the employed algorithm through analysis of the total energy expectation value, in terms of deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

The purpose of this study is to apply the distribution function formalism to the problem of electronic transport in open systems, and numerically solve the kinetic equation with a dissipation term. This term is modeled within the relaxation time approximation, and contains two parts, corresponding to elastic or inelastic processes. The collision operator is approximated as a sum of the semiclassical energy dissipation term, and the momentum relaxation term which randomizes momentum but does not change energy. As a result, the distribution of charge carriers changes due to the dissipation processes, which has a profound impact on the electronic transport through the simulated region discussed in terms of the current–voltage characteristics and their modification caused by the scattering.

Using the phase space approach, we consider the dynamics of a quantum particle in an isolated confined quantum system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the used algorithm by analysis of the total energy expectation value, in terms of the deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.

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.

We develop a method to calculate left-right eigenvector correlations of the product of $m$ independent $N\times N$ complex Ginibre matrices. For illustration, we present explicit analytical results for the vector overlap for a couple of examples for small $m$ and $N$. We conjecture that the integrated overlap between left and right eigenvectors is given by the formula $O = 1 + (m/2)(N-1)$ and support this conjecture by analytical and numerical calculations. We derive an analytical expression for the limiting correlation density as $N\rightarrow \infty$ for the product of Ginibre matrices as well as for the product of elliptic matrices. In the latter case, we find that the correlation function is independent of the eccentricities of the elliptic laws., Comment: 25 pag., 8 fig - Typos fixed, minor improvements in presentation

A mathematical model of the investigated semiconductor core-shell nanowire transistor with all-around gate, computation methods and calculated transport characteristics of the device are presented. The influence of applied gate voltage and drain-source voltage on the potential energy profile of the system is determined, electric current flowing through it is calculated and dependence of operation regime of the device on these voltages is discussed.

A controlled manipulation of electron spin states has been investigated for a cylindrical two-dimensional electron gas confined in a semiconductor nanotube/cylindrical nanowire with the Rashba spin–orbit interaction. We present analytical solutions for the two limiting cases, in which the spin–orbit interaction results from (A) the radial electric field and (B) the electric field applied along the z -axis of the nanotube. In the case (A), we have found that only the superposition of bands with the same orbital momentum leads to the spin precession around the cylinder (nanotube) axis. In the case (B), we have obtained the damped oscillations of the z spin component with the period that changes as a function of the coordinate z . We have shown that the damped oscillations of the average value of the z spin component form beats localized along the nanotube axis. The position of the beats can be controlled by the bias voltage.

A modification of the Blonder–Tinkham–Klapwijk (BTK) model is proposed for the description of the ferromagnet-superconductor interface. Modelling the contact potential with a rectangular barrier, we investigate the influence of the barrier width at the interface on the value of spin polarisation measured by point contact Andreev reflection. Results suggesting that neglecting the width of the barrier at the interface can lead to an overestimation of the spin polarisation using the original BTK model are presented. This effect is particularly strong for low values of polarization and vanishes for high polarisation. The impact on analysis of the experimental data is also discussed.

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.

We have studied the magnetotransport through an indium antimonide (InSb) nanowire grown in [111] direction, with a geometric constriction and in an external magnetic field applied along the nanowire axis. We have found that the magnetoresistance is negative for the narrow constriction, nearly zero for the constriction of some intermediate radius, and takes on positive values for the constriction with the radius approaching that of the nanowire. For all magnitudes of the magnetic field, the radius of constriction at which the change of the magnetoresistance sign takes place has been found to be almost the same as long as other geometric parameters of the nanowire are fixed. The sign reversing of the magnetoresistance is explained as a combined effect of two factors: the influence of the constriction on the transverse states and the spin Zeeman effect., Comment: 18 pages, 5 figures

Self-consistent Schrodinger–Poisson scheme is used to analyze the electronic transport in GaN/AlGaN nanowires containing a double-barrier structure within the Landauer formalism. Results of the calculations indicate that the exchange–correlation potential leads to emergence of Stark resonances in the transport window. The shot noise characterizing the current fluctuations reveals sub-Poissonian characteristics, significantly modified by the exchange–correlation contribution. As a consequence, we determine how geometric and material parameters affect those phenomena, which can be used to optimize the operation of such devices.

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 magnetoresistance in three-dimensional disordered systems formulated by Kawabata is discussed. The final form of the formula for the magnetoconductivity which is commonly used for fitting to the experiment has been proven to be incorrect and its agreement with experiment rather accidental. A revision of the theory of magnetoresistance is suggested.

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.

A spin- and time-dependent electron transport has been studied in a paramagnetic resonant tunneling diode using the self-consistent Wigner-Poisson method. Based on the calculated current-voltage characteristics in an external magnetic field we have demonstrated that under a constant bias both the spin-up and spin-down current components exhibit the THz oscillations in two different bias voltage regimes. We have shown that the oscillations of the spin-up (down) polarized current result from the coupling between the two resonance states: one localized in the triangular quantum well created in the emitter region and the second localized in the main quantum well. We have also elaborated the one-electron model of the current oscillations, which confirms the results obtained with the Wigner-Poisson method. The spin current oscillations can lower the effectiveness of spin filters based on the paramagnetic resonant tunneling structures and can be used to design the generators of the spin polarized current THz oscillations that can operate under the steady bias and constant magnetic field., 11 pages, 8 figures, to be published in Phys.Rev.B

Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the nonlinearity is explained in terms of energy levels anticrossings. The multifractal formalism is applied to investigate the effect of weak electric field on the statistical properties of electronic eigenfunctions. It is shown that the applied electric field does not remove the multifractal character of the electronic eigenfunctions, and that the singularity spectrum remains non-parabolic, however with a modified shape. Changes of the distances between energy levels of neighbouring eigenstates lead to the changes of the inverse participation ratio of the corresponding eigenfunctions in the weak electric field. It is demonstrated, that the local minima of the inverse participation ratio in the vicinity of the anticrossings correspond to discontinuity of the first derivative of the difference between marginal values of the singularity strength. Analysis of the generalized dimension as a function of the electric field shows that the electric field correlates spatial fluctuations of the neighbouring electronic eigenfunction amplitudes in the vicinity of anticrossings, and the nonlinear character of the scaling exponent confirms multifractality of the corresponding electronic eigenfunctions., Comment: 10 pages, 9 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.

The spin-dependent electron transport has been studied in magnetic semiconductor waveguides (nanowires) in the helical magnetic field. We have shown that -- apart from the known conductance dip located at the magnetic field equal to the helical-field amplitude $B_h$ -- the additional conductance dips (with zero conductance) appear at magnetic field different from $B_h$. This effect occuring in the non-adiabatic regime is explained as resulting from the resonant Landau-Zener transitions between the spin-splitted subbands., Comment: 5 pages, 7 figures

A simple model of chain containing Dirac’s delta-like potentials is used to calculate the density of states in systems with structural disorder. The crystal case of equally spaced scattering centers may be seen as a reference case suitable both for numerical calculations as well as analytical ones. The structural disorder means distortion of ideal lattice seen as fluctuation of distances between adjacent sites. Such disorder is sometimes referred to as amorphous and may lead to smearing off the band boundaries resulting in a tail-like density of states.

The dynamics of conduction electrons in resonant tunnelling nanosystems is studied within the phase-space approach based on the Wigner distribution function. The time evolution of the distribution function is calculated from the time-dependent quantum kinetic equation for which an effective numerical method is presented. Calculations of the transport properties of a double-barrier resonant tunnelling diode are performed to illustrate the proposed techniques. Additionally, analysis of the transient effects in the nanosystem is carried out and it is shown that for some range of the bias voltage the temporal variations of electronic current can take negative values. The explanation of this effect is based on the analysis of the time changes of the Wigner distribution function. The decay time of the temporal current oscillations in the nanosystem as a function of the bias voltage is determined.

Nonlinear properties of the spin-dependent electronic transport through a semiconductor resonant tunnelling diode with a paramagnetic quantum well are considered. The spin-dependent Wigner‐Poisson model of the electronic transport and the two-current Mott’s formula for the independent spin channels are applied to determine the current‐voltage curves of the nanodevice. Two types of the electronic current hysteresis loops are found in the current‐voltage characteristics for both the spin components of the electronic current. The physical interpretation of these two types of the electronic current hysteresis loops is given based on the analysis of the spin-dependent electron densities and the potential energy profiles. The differences between the current‐voltage characteristics for both the spin components of the electronic current allow us to explore the changes of the spin polarization of the current for different electric fields and determine the influence of the electronic current hysteresis on the spin polarization of the current flowing through the paramagnetic resonant tunnelling diode. (Some figures may appear in colour only in the online journal)

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 electronic transport characteristics of an asymmetric triple-barrier resonant tunnelling diode are calculated by the time-dependent Wigner–Poisson method. The intrinsic current oscillations are found in two separate bias voltage ranges. The first one is located below the resonant current peak, and the second lies in the negative differential resistance region. We provide the explanation of the current density oscillations in these two separate bias voltage ranges based on the analysis of the self-consistent potential profiles and changes of electron density. We have shown that two different formation mechanisms are responsible for the current density oscillations in these two bias voltage ranges. In the bias voltage range below the resonant current peak in the current–voltage characteristics, the current density oscillations are caused by the coupling between quasi-bound states in the left and right quantum wells. On the other hand, the current density oscillations in the negative differential resistance region result from the coupling between quasi-bound states in the left quantum well and the quantum well formed in the region of the left contact.

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.