Three-dimensional Quantum Wire Research Articles

Landau–Zener–Stückelberg–Majorana-like dynamics induced by tunneling of spin qubit states in a multiband two-state magnetic quantum wire

We investigate the transfer between spin quantum bit (qubit) states and study the Landau–Zener–Stückelberg–Majorana (LZSM)-like dynamics of tunneling spin qubits in a multiband two-state magnetic quantum wire. Indeed, within the framework of an optical parabolic potential in a three-dimensional (3D) heterostructure quantum wire and under the influence of an external time-varying magnetic field, a model for a multiband two-state magnetic quantum wire is developed. Here, the external magnetic field is used to coherently manipulate and control spin qubit states. By driving the system through an avoided crossing, we consider the associated effective quantum two-level system (TLS) related to the spin qubit states in each band, driving by an external coherent magnetic field in which the related Hamiltonian is Hermitian, and which generally paves a way to LZSM interferometry. Thus, we establish the analytical expressions of the energy eigenvalues in each band and derive the analytical solution of the dynamical evolution of the tunneling probabilities of the associated TLS. Accordingly, nonadiabatic and adiabatic tunneling probabilities (survival and transition) are calculated for each band of the multiband TLS. In this respect, the nonadiabatic and adiabatic dynamical evolutions of the tunneling probabilities of spin qubit populations in the first four bands, with band quantum numbers n = 0, 1, 2 and 3 are analyzed. As a result, depending on the amplitude strength of the driven magnetic field and the magnitude of the driving frequency, we report two striking nonadiabatic and adiabatic scenarios in each band for both the diabatic and adiabatic states. In this context, driving the two states of each band of the multiband TLS related to the spin qubit states through an avoided level crossing can result in nontrivial and incoherent dynamics at certain phases, resulting to apparent inaccurate probabilities, especially in the case of strong driven magnetic field and high driving frequency.

Simultaneous Effects of Temperature and Pressure on the Entropy and the Specific Heat of a Three-Dimensional Quantum Wire: Tsallis Formalism

In this work, the finite-difference time domain (FDTD) has been employed to calculate the energy levels and wave functions of a three-dimensional (3D) cylindrical quantum wire. The inside of the wire is at zero potential, and the background medium is 4.6 eV. This is a true 3D procedure based on a direct implementation of the time-dependent Schrodinger equation. Here, the dependence on the pressure and the temperature of the electronic effective mass is used. We study the effects temperature and pressure simultaneously on the entropy and the specific heat of the system using the Tsallis formalism. The results show that (i) the specific heat obtained by Tsallis has a peak structure. (ii) The entropy has almost the same values at very low temperatures with different pressures. (iii) The peak value of the specific heat with enhancing the pressure shifts toward lower temperatures. (iv) The peak value of the specific heat and its position depend on the value of the entropic index q.

Different effect of evanescent modes on acoustic phonon transport in different types of a three-dimensional quantum wire

By the use of the scattering matrix method, we investigate the effect of evanescent modes on acoustic phonon transport and thermal conductance in both convex and concave type three-dimensional quantum wire. Our results show that the evanescent modes can enhance the transmission coefficient and the thermal conductance in the concave type three-dimensional quantum wire. However, for the convex type three-dimensional quantum wire, the evanescent modes can play adverse effect on the phonon transport. When the length of scattering region is large enough, for all types of three-dimensional quantum wire, the influence of evanescent modes on phonon transport becomes very weak.

Ballistic thermal conductance in a three-dimensional quantum wire modulated with stub structure

Ballistic thermal conductance in a three-dimensional quantum wire with a stub structure is presented under both stress-free and hard wall boundary conditions at low temperatures. A comparative analysis for two-dimensional and three-dimensional models is made. The results show that when stress-free boundary conditions are applied, the universal quantum thermal conductance can be observed regardless of the geometry details in the limit T→0, and the behavior of the thermal conductance is qualitatively similar to that calculated by two-dimensional model. However, when hard wall boundary conditions are applied, the thermal conductance displays different behaviors in both two-dimensional and three-dimensional models.

Effects of effective mass discontinuity on the conductance of three-dimensional quantum wires

We calculate the conductance of three-dimensional semiconductor quantum wires considering different effective masses in the contacts and in the channel. We show that, with respect to the case with equal masses in the channel and in the contacts, the amplitude of the conductance oscillations increases if the electron effective mass in the channel is larger and decreases if it is smaller than in the contacts. Effects on the density of probability are also shown. These effects of the effective mass discontinuity are explained in terms of kinetic confinement and transmission coefficient modulation.

Fully Quantum Mechanical Simulations of Gated Silicon Quantum Wire Structures: Investigating the Effects of Changing Wire Cross-Section on Transport

We present transport simulations of three-dimensional (3D) silicon quantum wires in which electron-phonon scattering is incorporated via local modifications to the potential encountered by the electron waves. Computing resistance as a function of wire length, we find that the effects of dissipation essentially take hold immediately, and are apparent right from the point at which the wire is long enough to act as a true waveguide.

Hybrid impurity resonance in a three-dimensional Anisotropic quantum wire

The absorption of electromagnetic radiation of a three-dimensional quantum wire is theoretically investigated taking into account the processes associated with simultaneous scattering from ionized impurities. The absorption coefficient is studied as a function of the radiation frequency and the magnetic field strength. The shape of the absorption curve is analyzed.

Quasi-ballistic electron transport in quantum wires

Electron transport in a three-dimensional quantum wire is analyzed by taking into account electron scattering by a single point impurity. It is shown that the magnetoconductance plotted versus chemical potential μ has narrow peaks and closely located peaks separated by a dip when the scattering length is positive and negative, respectively. The peaks lie near the conductance steps. The thermopower plotted versus μ has narrow peaks and closely located peaks separated by a dip when the scattering length is positive and negative, respectively.

Thermopower of three-dimensional quantum wires and constrictions

The thermopower of asymmetrical quantum wires and constrictions in an arbitrarilydirected magnetic field is investigated. An analytic expression convenient for analysing thethermopower is obtained. The oscillations in the thermopower are studied. It is shown thatthe thermopower as a function of a magnetic field can undergo Aharonov–Bohm andShubnikov–de Haas oscillations.

Bound States for the Three-Dimensional Aharonov-Bohm Quantum Wire

The existence of bound states for the three-dimensional Aharonov-Bohm quantum wire, suggested by Dunne and Jaffe, is established provided the wire is thin enough. Recent results on the Aharonov-Bohm Schrodinger operator on a disk are used.

Shape effects on scattering in quantum wires with a transverse magnetic field

We investigate the effects of the shape of the cross section of a three-dimensional quantum wire on electron scattering from a single-point impurity, in the presence of a transverse magnetic field. Assuming parabolic confining potential of frequencies ${\ensuremath{\omega}}_{x}$ and ${\ensuremath{\omega}}_{y},$ it is shown that a magnetic field oriented along the small axis of the cross section of the wire produces the strongest effect on the conductance through the impurity (that is, the conductance is greatly enhanced). In the opposite case, it is shown that a magnetic field oriented along the large axis of the cross section of the wire produces the weakest effect (that is, the conductance is suppressed). The influence of the cross-sectional shape on the conductance versus the strength of the magnetic field is also considered and a magnetic blockade of electron transmission through the impurity is demonstrated. We further show that as the cross-sectional shape of the wire becomes asymmetric (i.e., as s increases, where $s={\ensuremath{\omega}}_{y}/{\ensuremath{\omega}}_{x}),$ switching of the conductance to different levels occurs. We use the Lippmann-Schwinger equation in order to calculate analytically the transmission coefficients.

Shape effects on scattering in three-dimensional quantum wires

We study the effects of the shape of the cross section of a three-dimensional quantum wire on electron scattering from a single point defect in the wire. The confinement of electrons is modeled by both hard- and soft-wall potentials. We find that as the degree of anisotropy of the cross section of the wire is increased intersubband electron scattering is enhanced and intrasubband transmission is suppressed making it appear as though the defect has stronger impact on electron scattering for asymmetric cross sections. Also, increasing the anisotropy of the cross section results in a decrease of the values of the conductance. Furthermore, for the soft-wall confinement the conductance as a function of Fermi energy rises faster than the conductance for the hard-wall confinement. We use the Lippmann–Schwinger equation of scattering theory in order to calculate analytically the transmission coefficients.

Quantization of the conductance of a three-dimensional quantum wire in the presence of a magnetic field

We study the ballistic transport in a three-dimensional quantum wire subjected to a uniform magnetic field of an arbitrary direction. The case of an elliptic cross section of the wire is considered. The temperature smearing of conductance quantization of the wire is analyzed.

Conductance of a quantum wire in a parallel magnetic field

Ballistic electron transport in a three-dimensional quantum wire with elliptic cross section is investigated. The potential of the single-particle Hamiltonian of the system under consideration was chosen to be parabolic. Using the Landauer-Buttiker formalism, we find an expression for the conductance at zero temperature. We show that the number and width of the steps in the dependence of the conductance on the electron energy are determined by the ratio of the characteristic frequencies of the potential. In the case of nonzero temperature we show that the conductance consists of two terms. The first is monotonic and depends quadratically on the energy; the oscillating second term gives sawtooth-shaped peaks. The height of the conductance steps is equal to the conductance quantum, and the width of the plateau depends on the energy, the field, and the frequency ratio. We stress that the picture of the conductance is extremely sensitive to the ratio of hybrid frequencies.

A parallel Green's operator for multidimensional quantum scattering calculations

A parallel algorithm for computing multidimensional scattering wave functions is introduced. The inhomogeneous scattering (Lippmann–Schwinger) equation is solved within the discrete variable representation with absorbing boundary conditions, using iterative (Krylov) methods. A parallel Green's operator enables one to distribute the wave function to orthogonal subspaces in which it is processed in parallel. Application to a model problem of electron scattering in a three-dimensional rectangular quantum wire is given. Speedup is demonstrated with an increasing number of processors and with increasing dimensions and/or sampling density. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 167–173, 1998

Reflection and Transmission Coefficients for Two- and Three-Dimensional Quantum Wires

The problem of a quantum wire connected smoothly on both sides to leads of variable cross section is studied. A method for solving this problem in terms of a set of nonlinear first order matrix differential equations for the variable reflection amplitude is discussed. The reflection coefficient obtained in this way is directly related to the conductivity, and is calculated as a function of the energy of the ballistic electrons. This formulation can be applied to three-dimensional as well as two dimensional quantum wires. For two specific cases the reflection coefficient is obtained as a function of the wave number of the incident electron, and the contribution of quantum tunneling to the transmission in each case is demonstrated. Also a model with a dissipative force is introduced and its effect on the transmission of the electrons is investigated.

Bound states in three-dimensional quantum wires

We have studied two different cylindrical waveguides with variable cross sections as models for quantum wires. By expanding the total wavefuction in terms of the Bessel function we have obtained an infinite set of coupled equations for the partial wave amplitude. In our models, bound states are present only in the lowest partial wave. For a simple bulge we have obtained the lowest eigenvalues, and for periodic waveguide we have found the width of the energy band.

Calculation of the residual resistivity of three-dimensional quantum wires.

Calculation of the residual resistivity of three-dimensional quantum wires.

Elastic electron transmission by barriers in a three-dimensional model quantum wire.

Numerical solutions of the time-dependent and time-independent Schr\odinger equations for electron tunneling in a three-dimensional model quantum wire have been carried out and used to calculate transmission probabilities over a range of energies. The model simulates a quantum heterostructure corresponding to a cylindrically symetric wire constructed from two different materials such that square barriers to the axial (z) motion occur in the disjoint region B=(${\mathit{z}}_{1}$\ensuremath{\le}z\ensuremath{\le}${\mathit{z}}_{2}$)\ensuremath{\cup}(${\mathit{z}}_{3}$\ensuremath{\le}z\ensuremath{\le}${\mathit{z}}_{4}$). In addition, the electron is bound harmonically in the radial distance r transverse to the longitudinal axis z; the electron vibrational frequency changes discontinuously from ${\mathrm{\ensuremath{\omega}}}_{\mathit{A}}$ in the disjoint region A=(-\ensuremath{\infty}z${\mathit{z}}_{1}$)\ensuremath{\cup}(${\mathit{z}}_{2}$z${\mathit{z}}_{3}$)\ensuremath{\cup}(${\mathit{z}}_{4}$z\ensuremath{\infty}) to ${\mathrm{\ensuremath{\omega}}}_{\mathit{B}}$ in the disjoint region B.