Effects of magnetic field on the electronic structure of wurtzite quantum dots: Calculations using effective-mass envelope function theory

The Hamiltonian of the wurtzite quantum dots in the presence of an external homogeneous magnetic field is given. The electronic structure and optical properties are studied in the framework of effective-mass envelope function theory. The energy levels have new characteristics, such as parabolic property, antisymmtric splitting, and so on, different from the Zeeman splitting. With the crystal field splitting energy Delta(c)=25 meV, the dark excitons appear when the radius is smaller than 25.85 A in the absence of external magnetic field. This result is more consistent with the experimental results reported by Efros [Phys. Rev. B 54, 4843 (1996)]. It is found that dark excitons become bright under appropriate magnetic field depending on the radius of dots. The circular polarization factors of the optical transitions of randomly oriented dots are zero in the absence of external magnetic field and increase with the increase of magnetic field, in agreement with the experimental results. The circular polarization factors of single dots change from nearly 0 to about 1 as the orientation of the magnetic field changes from the x axis of the crystal structure to the z axis, which can be used to determine the orientation of the z axis of the crystal structure of individual dots. The antisymmetric Hamiltonian is very important to the effects of magnetic field on the circular polarization of the optical transition of quantum dots.

Quantum master-equation approach to quantum transport through mesoscopic systems

For quantum transport through mesoscopic systems, a quantum master-equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of Gurvitz's approach for quantum transport and quantum measurement, namely, to finite temperature and arbitrary bias voltage. Our derivation starts from a second-order cumulant expansion of the tunneling Hamiltonian; then follows the conditional average over the electrode reservoir states. As a consequence, in the usual weak-tunneling regime, the established formalism is applicable for a wide range of transport problems. The validity of the formalism and its convenience in application are well illustrated by a number of examples.

Spin-polarized tunneling through a diluted magnetic semiconductor quantum dot

Spin-polarized tunneling through a diluted magnetic semiconductor quantum dot embedded in a tunneling barrier is investigated using the Bardeen transfer Hamiltonian. The tunneling current oscillates with an increasing magnetic field for a fixed bias. Many peaks are observed with an increasing external bias under a fixed magnetic field. Spin polarization of the tunneling current is tuned by changing the external bias under a weak magnetic field.

Excitonic energy of vertically stacked self-assmbled InAs quantum dots

We have studied the exciton states in vertically stacked self-assembled quantum disks within the effective mass approximation. The energy spectrum of the electron and hole is calculated using the transfer matrix formalism in the adiabatic approximation. The Coulomb interaction between the electron and the hole is treated accurately by the direct diagonalization of the Hamiltonian matrix. The effect of the vertical alignment of the disks on the ground energy of heavy- and light-hole exciton is presented and discussed. The binding energy is discussed in terms of the probability of the ground wave function. The ground energy of heavy- and light-hole excitons as a function of the magnetic field is presented and the effect of the disk size (the radius of disks) on the exciton energy is discussed.

Role of interactions in electronic structure of a two-electron quantum dot molecule

We have studied a two-electron quantum dot molecule in a magnetic field. The electron interaction is treated accurately by the direct diagonalization of the Hamiltonian matrix. We calculate two lowest energy levels of the two-electron quantum dot molecule in a magnetic field. Our results show that the electron interactions are significant, as they can change the total spin of the two-electron ground state of the system by adjusting the magnetic field between S = 0 and S = 1. The energy difference DeltaE between the lowest S = 0 and S = 1 states is shown as a function of the axial magnetic field. We found that the energy difference between the lowest S = 0 and S = 1 states in the strong-B S = 0 state varies linearly. Our results provide a possible realization for a qubit to be fabricated by current growth techniques.

Calculation of energy levels in InGaAs/GaAs quantum dot array

The subbands of the ground state E-c1, the first excited state E-c2 and heavy hole state E-HH1 are calculated by solving the eigenvalues of effective-mass Hamiltonian H-0 which is derived from eight-band k . p theory and the calculations are performed at k(x) = k, = k = 0 for the three-dimensional array of InGaAs/GaAs quantum dots (QDs). With indium content in InGaAs QDs gradually increasing from 30% to 100%,the intersubband transition wavelength of E-c2 to E-c1, blue-shifts from 18.50 to 11.87 mu m,while the transition wavelength of E-c1, to E-HH1, red-shifts from 1. 04 to 1. 73 mu m. With the sizes of Ir-0.5 Ga-0.5 As and InAs QDs increasing from 1.0 to 5.0 nm, the intersubband transition from E-c1, to E-C2 transforms from bound-state-to-continuum-state to bound-state-to-bound-state, and the corresponding intersubband transition wavelengths red-shift from 8.12 pm (5.90 pm) to 53.47 mu m (31.87 pm), respectively, and the transition wavelengths of E-C1 to E-HH1 red-shift from 1. 13 mu m (1.60 mu m) to 1.27 mu m (2.01 mu m), respectively.

Spin states and persistent currents in mesoscopic rings: Spin-orbit interactions

We investigate theoretically electron spin states in one-dimensional and two-dimensional (2D) hard-wall mesoscopic rings in the presence of both the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI) in a perpendicular magnetic field. The Hamiltonian of the RSOI alone is mathematically equivalent to that of the DSOI alone using an SU(2) spin rotation transformation. Our theoretical results show that the interplay between the RSOI and DSOI results in an effective periodic potential, which consequently leads to gaps in the energy spectrum. This periodic potential also weakens and smoothens the oscillations of the persistent charge current and spin current and results in the localization of electrons. For a 2D ring with a finite width, higher radial modes destroy the periodic oscillations of persistent currents.

Giant Zeeman splitting in manganese-doped ZnSe quantum spheres: Eight-band effective-mass calculations

We deduce the eight-band effective-mass Hamiltonian model for a manganese-doped ZnSe quantum sphere in the presence of the magnetic field, including the interaction between the conduction and valence bands, the spin-orbit coupling within the valence bands, the intrinsic spin Zeeman splitting, and the sp-d exchange interaction between the carriers and magnetic ion in the mean-field approximation. The size dependence of the electron and hole energy levels as well as the giant Zeeman splitting energies are studied theoretically. We find that the hole giant Zeeman splitting energies decrease with the increasing radius, smaller than that in the bulk material, and are different for different J(z) states, which are caused by the quantum confinement effect. Because the quantum sphere restrains the excited Landau states and exciton states, in the experiments we can observe directly the Zeeman splitting of basic states. At low magnetic field, the total Zeeman splitting energy increases linearly with the increasing magnetic field and saturates at modest field which is in agreement with recent experimental results. Comparing to the undoped case, the Zeeman splitting energy is 445 times larger which provides us with wide freedom to tailor the electronic structure of DMS nanocrystals for technological applications.

Optical properties and g factors of GaAs quantum rods

The Hamiltonian of the zinc-blende quantum rods in the framework of eight-band effective-mass approximation in the presence of external homogeneous magnetic field is given. The electronic structure, optical properties and electron g factors of GaAs quantum rods are investigated. We found that the electron g factors are very sensitively dependent on the dimensions of the quantum rods. As some of the three dimensions increase, the electron g factors decrease. The more the dimensions increase, the more the electron g factors decrease. The dimensions perpendicular to the direction of the magnetic field affect the electron g factors more than the other dimension. (c) 2006 Elsevier B.V. All rights reserved.

Electronic structure and g factors of narrow-gap zinc-blende nanowires and nanorods

The Hamiltonian in the framework of eight-band effective-mass approximation of the zinc-blende nanowires and nanorods in the presence of external homogeneous magnetic field is given in the cylindrical coordinate. The electronic structure, optical properties, magnetic energy levels, and g factors of the nanowires and nanorods are calculated. It is found that the electron states consist of many hole-state components, due to the coupling of the conduction band and valence band. For the normal bands which are monotone functions of |k(z)|, long nanorods can be modeled by the nanowires, the energy levels of the nanorods approximately equal the values of the energy band E(k(z)) of the nanowires with the same radius at a special k(z), where k(z) is the wave vector in the wire direction. Due to the coupling of the states, some of the hole energy bands of the nanowires have their highest points at k(z)=0. Especially, the highest hole state of the InSb nanowires is not at the k(z)=0 point. It is an indirect band gap. For these abnormal bands, nanorods can not be modeled by the nanowires. The energy levels of the nanorods show an interesting plait-like pattern. The linear polarization factor is zero, when the aspect ratio L/2R is smaller than 1, and increases as the length increases. The g(z) and g(x) factors as functions of the k(z), radius R and length L are calculated for the wires and rods, respectively. For the wires, the g(z) of the electron ground state increases, and the g(z) of the hole ground state decreases first, then increases with the k(z) increasing. For the rods, the g(z) and g(x) of the electron ground state decrease as the R or the L increases. The g(x) of the hole ground state decreases, the g(z) of the hole ground state increases with the L increasing. The variation of the g(z) of the wires with the k(z) is in agreement with the variation of the g(z) of the rods with the L.

Electronic states in InAs quantum spheres and ellipsoids

The eight-band effective-mass Hamiltonian of the free-standing narrow-gap InAs quantum ellipsoids is developed, and the electron and hole electronic structures as well as optical properties are calculated by using the model. The energies, wave functions and transition probabilities of quantum spheres as functions of the radius of quantum sphere R is presented. It is found that the energy levels do not vary as 1/R-2, which is caused by the coupling between the conduction and valence bands, and by the constant terms correspond to the spin-orbit splitting energy. The blueshifts of hole states depend strongly on the coupling from electron states, so that the order of hole states changes as has been predicted in experiment. The exciton binding energies are calculated, the calculated excitonic gaps as functions of the ground exciton transition energy are in good agreement with the photoluminescence measured spectra in details. Finally, the hole energy levels and the linear polarization factors in InAs quantum ellipsoids as functions of the aspect ratio are presented. The state 1S(Z up arrow)((1/2)) becomes the hole ground state when e is larger than 2.4. The saturation value of the linear polarization factors of the InAs long ellipsoids of diameter 2.0 nm is 0.86, in agreement with the experimental results.

Electronic structures of wurtzite ZnO and ZnO/MgZnO quantum well

The band structures of wurtzite ZnO are calculated using the empirical pseudopotential method (EPM). The 8 parameters of the Zn and O atom pesudopotential form factors with Schluter's formula are obtained. The effective mass parameters are extracted by using k.p Hamiltonian to fit the EPM results. The calculated band edge energies (E-g, E-A, E-B, and E-C) at Gamma point are in good agreement with experimental results. The ordering of ZnO at the top of valence band is found to be A(Gamma(7))-B(Gamma(9))-C(Gamma(7)) due to a negative spin-orbit (SO) splitting. Based on the band parameters obtained, the valence hole subbands of wurzite ZnO/MgxZn1-xO tensile-strained quantum wells (QWs) with different well widths and Mg compositions are calculated using 6-band k.p method. (c) 2005 Elsevier B.V. All rights reserved.

Origin and elimination of spurious solutions of the eight-band k center dot p theory

The origin of spurious solutions in the eight-band envelope function model is examined and it is shown that spurious solutions arise from the additional spurious degeneracies caused by the unphysical bowing of the conduction bands calculated within the eight-band k center dot p model. We propose two approaches to eliminate these spurious solutions. Using the first approach, the wave vector cutoff method, we demonstrate the origin and elimination of spurious solutions in a transparent way without modifying the original Hamiltonian. Through the second approach, we introduce some freedom in modifying the Hamiltonian. The comparison between the results from the various modified Hamiltonians suggests that the wave vector cutoff method can give accurate enough description to the final results.

Effects of electric field on the electronic structure and optical properties of quantum rods with wurtzite structure

The Hamiltonian of wurtzite quantum rods with an ellipsoidal boundary under electric field is given after a coordinate transformation. The electronic structure and optical properties are studied in the framework of the effective-mass envelope-function theory. The quantum-confined Stark effect is illustrated by studying the change of the electronic structures under electric field. The transition probabilities between the electron and hole states decrease sharply with the increase of the electric field. The polarization factor increases with the increase of the electric field. Effects of the electric field and the shape of the rods on the exciton effect are also investigated. The exciton binding energy decreases with the increase of both the electric field and the aspect ratio. In the end, considering the exciton binding energy, we calculated the band gap variation of size- and shape-controlled colloidal CdSe quantum rods, which is in good agreement with experimental results.

Electronic structure and optical properties of quantum rods with wurtzite structure

The Hamiltonian of the wurtzite quantum rods with an ellipsoidal boundary is given after a coordinate transformation. The energies, wave functions, and transition possibilities are obtained as functions of the aspect ratio e with the same method we used on spherical dots. With an overall consideration of both the transition matrix element and the Boltzmann distribution we explained why the polarization factor increases with increasing e and approaches a saturation value, which tallies quite well with the experimental result. When e increases more and more S-z states are mixed into the ground, second, and third states of J(z)=1/2, resulting in an increase of the emission of z polarization. It is just the linear terms of the momentum operator in the hole Hamiltonian that cause the mixing of S and P states in the hole ground state. The effects of the crystal field splitting energy, temperature, and transverse radius to the polarization are also considered. We also calculated the band gap variation with the size and shape of the quantum rods.