Electron-electron scattering in a double quantum dot: Effective mass approach (original) (raw)
A quasi-analytical approach to study energy levels of a two-electron quantum dot
The European Physical Journal B, 2010
Our approach is quasi-analytical. We consider the Hamiltonian of a two-electron quantum dot composed of quadratic plus Coulomb terms as well as a term related to the interaction with the external magnetic field. To avoid the complexity, the Taylor expansion of the effective potential is introduced into the problem and thereby a solution is found for the eigenvalues of the corresponding two-body Schrödinger equation in terms of the Wigner parameter. We have finally made a comparison with some other theoretical results.
Physical Review B, 2007
We have developed a theoretical method to study scattering processes of an incident electron through an N-electron quantum dot (QD) embedded in a two-dimensional (2D) semiconductor. The generalized Lippmann-Schwinger equations including the electron-electron interaction in this system are solved for the continuum electron by using the method of continued fractions (MCF) combined with 2D partial wave expansion technique. The method is applied to a one-electron QD case. Scattering cross-sections are obtained for both the singlet and triplet couplings between the incident electron and the QD electron during the scattering. The total elastic scattering cross-sections as well as the spin-flip scattering cross-sections resulting from the exchange potential are presented. Furthermore, inelastic scattering processes are also studied using a multichannel formalism of the MCF.
Electron dynamics in rectangular double quantum dots
Nanotechnology, 2006
The temporal evolution of an electron in a double rectangular quantum dot in the presence of an electric field pulse is explored in this work. In the framework of the effective mass approximation, first-order scattering rates for electron–electron and electron–longitudinal acoustic phonon interaction at room temperature are calculated in the high tunnelling regime, and used to evaluate the dynamics of the population and coherence of the first three confined levels under an electric field pulse. Small values of these rates dependent upon the coupling barrier make feasible the emission of coherent radiation near 0.1 THz.
Physical Review B, 2013
We calculated Coulomb scattering rates from quantum dots (QDs) coupled to a 2D carrier reservoir and QDs coupled to a 3D reservoir. For this purpose, we used a microscopic theory in the limit of Born-Markov approximation, in which the numerical evaluation of high dimensional integrals is done via a quasi-Monte Carlo method. Via a comparison of the so determined scattering rates, we investigated the question whether scattering from 2D is generally more efficient than scattering from 3D. In agreement with experimental findings, we did not observe a significant reduction of the scattering efficiency of a QD directly coupled to a 3D reservoir. In turn, we found that 3D scattering benefits from it's additional degree of freedom in the momentum space.
Journal of Physics: Conference Series, 2013
Magnetic-field dispersion of the multiexcitons related to the p shell of a single quantum dot (QD) is analysed in this work. The reduced cyclotron effective mass of carriers is determined from the energy splitting between the p+-and p−-related multiexcitonic emission lines. The reduced mass in the occupied QD was found to be larger than the mass related to the QD's single particle structure. The apparent increase of the reduced mass with increasing excitonic occupation of the dot is related to the mass renoralization due to electron-electron interactions within a multiexcitonic droplet.
Coupling effects on electron-phonon scattering in double quantum dots
Physica Status Solidi C, 2007
In this work we study the electron-phonon interaction in GaAs/AlGaAs double-dot systems for cylindrical and spherical geometries with finite confinement, coupled by a tunnelling barrier and an external dc electric field. The eigenenenergies and envelope wave functions are numerically obtained for different values of the external bias. We study the effects of field and the dots-shape on the relaxation rates of electronic transitions between double-dot states by electron-acoustic phonon and electron-optical phonon interaction. We found the piezoelectric interaction to be small compared with the deformation potential one, and the spherical more convenient than the cylindrical geometry to reduce the electron-phonon decay rates.
Two Electrons in a Quantum Dot: A Unified Approach
International Journal of Theoretical Physics, 2008
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.
Two-electron quantum dot model revisited: bound states and other analytical and numerical solutions
The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In particular, some corrections are also made in previous theoretical calculations. The corrected polynomial solutions are confronted with numerical calculations based on the Numerov method, in a good agreement between both. Then, new solutions considering the 1/r and ln r Coulombian-like potentials in (1+2)D, not yet obtained, are discussed numerically. In particular, we are able to calculate the quantum dot eigenfunctions for a much larger spectrum of external harmonic frequencies as compared to previous results. Also the existence of bound states for such planar system in the case l = 0 is predicted and the respective eigenvalues are determined.
Resonance states of two-electron quantum dots
Physical Review B, 2005
Autoionizing resonance states of two-electron quantum dots are studied by using the effective-mass complex-eigenvalue equation approach. It is shown that two-electron quantum dots may have very rich spectra of resonance states. The number of them and their lifetimes depend strongly on the dot size. It is observed that a resonance state may change its character from Feshbach to shape type with the dot size decreasing. Since the resonance states may have very long lifetimes they should not be neglected in the description of transport processes in quantum dots.
Photoemission From A Two Electron Quantum Dot
We consider photoemision from a two-electron quantum dot and find analytic expression for the cross-section. We show that the emission cross-section from the ground state as a function of the magnetic field has sharp discontinuities corresponding to the singlet-triplet transitions for low magnetic fields and the transitions between magic numbers (2J+1) for high magnetic field. We also find the corrections to the photoemission cross-section from a more relistic quantum dot having a finite thickness due to nonvanishing extent of electron wave function in the direction perpendicular to the plane in which 2-D dot electrons are usually confined. Artificial atoms or quantum dots, which are essentially electrons confined in a two-dimensional region with a magnetic field in the third direction have been the subject of intense experimental and theoretical activity over the last few years . The artificial "hydrogen atom" (single electron confined in a circular region by a harmonic potential with a magnetic field in the perpendicular direction) was solved for the eigenvalues and eigenfunctons over seventy years ago by Fock . The levels were experimentally observed [3] more than fifty years later with the advent of quantum dots. The artificial "helium atom" (two electrons confined in a circular region by a harmonic potential with a magnetic field in the third direction) was tackled sixty years after the hydrogen atom. Maksym and Chakraborty [4] and Wagner, Merkt and Chaplik [5] worked out the energy levels and found an incredibly rich structure. The ground state can change its parity as the magnetic field is changed and there can be singlet-triplet transition. However, spectroscopic studies did not reveal the spectacular features because of an effect noted by these authors [4], . Instead, they relied on certain thermodynamic