On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

Density-potential mapping in the standard and quantum electrodynamical time-dependent density functional theory

131 p.

One-dimensional quantum waveguide theory of Rashba electrons

The ballistic spin transport in one-dimensional waveguides with the Rashba effect is studied. Due to the Rashba effect, there are two electron states with different wave vectors for the same energy. The wave functions of two Rashba electron states are derived, and it is found that their phase depend on the direction of the circuit and the spin directions of two states are perpendicular to the circuit, with the +pi/2 and -pi/2 angles, respectively. The boundary conditions of the wave functions and their derivatives at the intersection of circuits are given, which can be used to investigate the waveguide transport properties of Rashba spin electron in circuits of any shape and structure. The eigenstates of the closed circular and square loops are studied by using the transfer matrix method. The transfer matrix M(E) of a circular arc is obtained by dividing the circular arc into N segments and multiplying the transfer matrix of each straight segment. The energies of eigenstates in the closed loop are obtained by solving the equation det[M(E)-I]=0. For the circular ring, the eigenenergies obtained with this method are in agreement with those obtained by solving the Schrodinger equation. For the square loop, the analytic formula of the eigenenergies is obtained first The transport properties of the AB ring and AB square loop and double square loop are studied using the boundary conditions and the transfer matrix method In the case of no magnetic field, the zero points of the reflection coefficients are just the energies of eigenstates in closed loops. In the case of magnetic field, the transmission and reflection coefficients all oscillate with the magnetic field; the oscillating period is Phi(m)=hc/e, independent of the shape of the loop, and Phi(m) is the magnetic flux through the loop. For the double loop the oscillating period is Phi(m)=hc/2e, in agreement with the experimental result. At last, we compared our method with Koga's experiment. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3253752]

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.

Effective-mass theory for hierarchical self-assembly of GaAs/AlxGa1-xAs quantum dots

The electronic structures in the hierarchical self-assembly of GaAs/AlxGa1-xAs quantum dots are investigated theoretically in the framework of effective-mass envelope function theory. The electron and hole energy levels and optical transition energies are calculated. In our calculation, the effect of finite offset, valence-band mixing, the effects due to the different effective masses of electrons and holes in different regions, and the real quantum dot structures are all taken into account. The results show that (1) electronic energy levels decrease monotonically, and the energy difference between the energy levels increases as the GaAs quantum dot (QD) height increases; (2) strong state mixing is found between the different energy levels as the GaAs QD width changes; (3) the hole energy levels decrease more quickly than those of the electrons as the GaAs QD size increases; (4) in excited states, the hole energy levels are closer to each other than the electron ones; (5) the first heavy- and light-hole transition energies are very close. Our theoretical results agree well with the available experimental data. Our calculated results are useful for the application of the hierarchical self-assembly of GaAs/AlxGa1-xAs quantum dots to photoelectric devices.

Electronic structure of Mn-doped ZnO quantum wires: A mean-field theory study

Based on the effective-mass model and the mean-field approximation, we investigate the energy levels of the electron and hole states of the Mn-doped ZnO quantum wires (x=0.0018) in the presence of the external magnetic field. It is found that either twofold degenerated electron or fourfold degenerated hole states split in the field. The splitting energy is about 100 times larger than those of undoped cases. There is a dark exciton effect when the radius R is smaller than 16.6 nm, and it is independent of the effective doped Mn concentration. The lowest state transitions split into six Zeeman components in the magnetic field, four sigma(+/-) and two pi polarized Zeeman components, their splittings depend on the Mn-doped concentration, and the order of pi and sigma(+/-) polarized Zeeman components is reversed for thin quantum wires (R < 2.3 nm) due to the quantum confinement effect.

Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nanoelectronic devices

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master equation with the well-known time-dependent density functional theory. The key ingredients of this paper include (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e., the device); and (iii) the construction of Kohn-Sham master equations for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOMs) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along with the propagation of the Kohn-Sham master equation and the EOMs of the auxiliary functions.

Effective-mass theory for coupled quantum dots grown on (11N)-oriented substrates

The electronic structures of coupled quantum dots grown on (11N)-oriented substrates are studied in the framework of effective-mass envelope-function theory. The results show that the all-hole subbands have the smallest widths and the optical properties are best for the (113), (114), and (115) growth directions. Our theoretical results agree with the available experimental data. Our calculated results are useful for the application of coupled quantum dots in photoelectric devices.

Theory of ultrafast optical manipulation of electron spins in quantum wells

Based on a multiparticle-state stimulated Raman adiabatic passage approach, a comprehensive theoretical study of the ultrafast optical manipulation of electron spins in quantum wells is presented. In addition to corroborating experimental findings [Gupta , Science 292, 2458 (2001)], we improve the expression for the optical-pulse-induced effective magnetic field, in comparison with the one obtained via the conventional single-particle ac Stark shift. Further study of the effect of hole-spin relaxation reveals that, while the coherent optical manipulation of electron spin in undoped quantum wells would deteriorate in the presence of relatively fast hole-spin relaxation, the coherent control in doped systems can be quite robust against decoherence. The implications of the present results on quantum dots will also be discussed. (c) 2005 American Institute of Physics.

Quantum waveguide theory for hole transport in mesoscopic structures

A quantum waveguide theory is proposed for hole transport in the mesoscopic structures, including the band mixing effect. We found that due to the interference between the 'light' hole and 'heavy' wave, the transmission and reflection coefficients oscillate more irregularly as a function of incident wave vector geometry parameters. Furthermore conversion between the heavy hole and light hole states occurs at the intersection. (C) 2003 Elsevier Ltd. All rights reserved.

Resonant tunneling theory of planar quantum dot structures

The ballistic transport in the semiconductor, planar, circular quantum dot structures is studied theoretically. The transmission probabilities show apparent resonant tunneling peaks, which correspond to energies of bound states in the dot. By use of structures with different angles between the inject and exit channels, the resonant peaks can be identified very effectively. The perpendicular magnetic field has obvious effect on the energies of bound states in the quantum dot, and thus the resonant peaks. The treatment of the boundary conditions simplifies the problem to the solution of a set of linear algebraic equations. The theoretical results in this paper can be used to design planar resonant tunneling devices, whose resonant peaks are adjustable by the angle between the inject and exit channels and the applied magnetic field. The resonant tunneling in the circular dot structures can also be used to study the bound states in the absence and presence of magnetic field.

EFFECTIVE-MASS THEORY FOR GAAS/GA1-XALXAS QUANTUM WIRES AND CORRUGATED SUPERLATTICES GROWN ON (311)-ORIENTED SUBSTRATES

The electronic structures of GaAs/Ga1-xAlxAs quantum wires (corrugated superlattices) grown on (311)-oriented substrates are studied in the framework of the effective-mass envelope-function method. The electron and hole subband structure and optical transition matrix elements are calculated. When x=1, the results are compared with experiments, and it is found that the direct transition becomes an indirect transition as the widths of well and barrier become smaller.

QUANTUM WAVE-GUIDE THEORY FOR MESOSCOPIC STRUCTURES

A one-dimensional quantum waveguide theory for mesoscopic structures is proposed, and the boundary conditions of the wave functions at an intersection are given. The Aharonov-Bohm effect is quantitatively discussed with use of this theory, and the reflection, transmission amplitudes, etc., are given as functions of the magnetic flux, the arm lengths, and the wave vector. It is found that the oscillating current consists of a significant component of the second harmonic. This theory is also applied to investigate quantum-interference devices. The results on the Aharonov-Bohm effect and the quantum-interference devices are found to be in agreement with previous theoretical results.