Wave Functions Of Quantum Dots Research Articles

Statistical model of electronic structure in InAs, InP, GaSb, and Si quantum dots with surface roughness

Simulations based on the sp 3 d 5 s * empirical tight-binding method were performed to provide a statistical understanding of the electronic structures and bandgap distributions of III–V (InAs, InP, GaSb) and IV (Si) semiconductor quantum dots (QDs) with surface roughness. The electronic states and wavefunctions of QDs with surface roughness of different sizes, shapes, and materials were computed. The effects of surface roughness on the electronic structures and the bandgap distributions of QDs were investigated. The results show that the bandgaps of QDs of considered materials/sizes/shapes increase on average when introducing surface roughness. It is shown that the simulated bandgap distributions of QDs with surface roughness can be reproduced by a simple model formula, which can be applied to different materials, sizes, and shapes. The model formula was derived by assuming that removing and adding of one atom procedures are independent random processes.

Modeling of electronic structure for dome-shaped quantum dots

A Hamiltonian operator in assessing the energy levels and wavefunctions of quantum dots (QDs) was proposed. The finite element method was used to solve the numerical Schrödinger equation for envelope function in the effective mass approximation. Within this model, we have investigated QDs with different geometries (cone, lens and dome-shaped dot). While it is easy to attain stability for conical QDs, it is difficult with lens QDs. Strain and mole-fraction effects are also studied. Our results coincide with the experimental one.

Control of Dynamic Properties of InAs/InAlGaAs/InP Hybrid Quantum Well‐Quantum Dot Structures Designed as Active Parts of 1.55 μm Emitting Lasers

The molecular beam epitaxy grown structures are investigated, comprising of InGaAs quantum wells (QW) separated by a thin InGaAlAs barrier from InAs quantum dots (QDs), emitting at 1.55 μm, grown on an InP substrate. To control the coupling between QW and QD parts the thickness of the barrier is changed, which commands the wave function overlap. The tuning of that parameter allows for the study of the influence of the QW potential on the energy structure of states and their wave functions in QDs, changing from an uncoupled system, where the optical response is just a sum of responses from two isolated elements, to a strongly quantum mechanically coupled system, exhibiting mixed 2D‐0D characteristics. The changes of the energy structure that are deduced from the photoreflectance and photoluminescence spectroscopy results, supported by 8‐band k · p modeling, explain the measured differences in the photoluminescence decay times between samples with different barrier thicknesses.

Fundamental mechanisms of the dependence of spin states on exchange correlations in quantum dots: Feynman path integrals

The effect of permutation symmetry of nonrelativistic electron wave functions in quantum dots on the spatial correlations, energy, and distribution over the spin states is investigated. The quantitative analysis is based on ab initio calculations using the technique of Feynman path integrals of entangled quantum states in model spherically symmetrical quantum dots with the parabolic confining field. In the computer simulation, the quantum-mechanical indistinguishability and spin variable are exactly taken into account. It is demonstrated that the detailed description of the high-order spatial correlations plays a key role in the correct calculation of the equilibrium spin number and energy values.

Transport in a three-terminal graphene quantum dot in the multi-level regime

We investigate transport in a three-terminal graphene quantum dot. All nine elements of the conductance matrix have been independently measured. In the Coulomb blockade regime, accurate measurements of individual conductance resonances reveal slightly different resonance energies depending on which pair of leads is used for probing. Rapid changes in the tunneling coupling between the leads and the dot due to localized states in the constrictions have been excluded by tuning the difference in resonance energies using in-plane gates which couple preferentially to individual constrictions. The interpretation of the different resonance energies is then based on the presence of a number of levels in the dot with an energy spacing of the order of the measurement temperature. In this multi-level transport regime, the three-terminal device offers the opportunity to sense if the individual levels couple with different strengths to the different leads. This in turn gives qualitative insight into the spatial profile of the corresponding quantum dot wave functions.

Magnetic field dependence of quantum dot ground states

We study the ground states of a planar quantum dot with N = 5 , 6 , 7 electrons, in the presence of a perpendicular magnetic field. Using a spatially unrestricted Hartree Fock technique followed by spin and angular momentum symmetry restoration, chemical potentials are calculated and transitions between different ground states are identified. A spin blockade in the 6 → 7 transition is found. The structure of the quantum dot wave functions is illustrated by their electron densities.

Correlation Effects in Quantum Dot Wave Function Imaging

We demonstrate that in semiconductor quantum dots wave functions, as imaged by local tunneling spectroscopies like STM, show characteristic signatures of electron-electron Coulomb correlation. We predict that such images correspond to “quasi-particle” wave functions which cannot be computed by standard mean-field techniques in the strongly correlated regime. From the configuration-interaction solution of the few-particle problem for prototype dots, we find that quasi-particle wave function images may display signatures of Wigner crystallization.

Maximum-density droplet to lower-density droplet transition in quantum dots

We show that the Landau level mixing in two-dimensional quantum dot wave functions can be taken into account very effectively by multiplying the exact lowest Landau level wave functions by a Jastrow factor which is optimized by variance minimization. The comparison between exact diagonalization and fixed phase diffusion Monte Carlo results suggests that the phase of the many-body wave functions are not affected much by Landau level mixing. We apply these wave functions to study the transition from the maximum density droplet state [incipient integer quantum Hall state with angular momentum $L=N(N\ensuremath{-}1)∕2$] to lower density droplet states $[L>N(N\ensuremath{-}1)∕2]$.

New analytical calculations of the resonance modes in lens-shaped cavities: applications to the calculations of the energy levels and electronic wavefunctions in quantum dots

The problem of the energy levels and electronic wavefunctions in quantum dots is studied in the parabolic coordinates system. A conventional effective mass Hamiltonian is written. For an infinite potential barrier, it is related to the more general problem of finding the resonance modes in a cavity. The problem is found to be separable for a biconvex-shaped cavity or quantum dot with an infinite potential barrier. This first shape of quantum dot corresponds to the intersection of two orthogonal confocal parabolas. Then plano-convex lens-shaped cavities or quantum dots are studied. This problem is no more separable in the parabolic coordinates but using symmetry properties, we show that the exact solutions of the problem are simple combinations of the previous solutions. The same approach is used for spherical coordinates and hemispherical quantum dots. It is finally shown that convex lens-shaped quantum dots give a good description of self-organized InAs quantum dots grown on InP.

Acoustic phonon problem in nanocrystal–dielectric matrix systems

It has been shown that the energy spectrum of acoustic phonons in semiconductor quantum dots (QDs) embedded in a dielectric matrix is continuous despite the three-dimensional spatial confinement. This immediately follows from the analysis of the vibrational spectrum of such composite material, treating the QDs and host matrix as a unified system. Then, the confinement only modifies the acoustic phonon wave functions in QDs as compared to the bulk. From this point of view the phonon sideband structure in optical spectra of the QDs has been analyzed.

Mapping the wave functions in quantum dots

We use magneto-tunnelling spectroscopy to investigate the form of the wave functions of the confined electron states in InAs self-assembled quantum dots. We are able to observe the wave functions corresponding to the ground and the two lowest excited states for dots grown on (1 0 0)- and (3 1 1)B-oriented GaAs substrates. For both orientations, the wave functions are found to have a biaxial symmetry in the growth plane, with axes parallel to main crystallographic directions. In addition, we have performed magneto-tunnelling spectroscopy measurements on tunnel diodes that incorporate gate electrodes. By observing how the energies of particular states vary with gate bias, we are able to identify the states associated with an individual dot. This allows us to measure quantitatively both the energy levels and wave functions of the dot states.

Magneto-Tunnelling Spectroscopy for Spatial Mapping of Orbital Wavefunctions of the Ground and Excited Electronic States in Self-Assembled Quantum Dots

We present an experimental study of electron wavefunctions in InAs/GaAs self-assembled quantum dots (QDs). Magneto-tunnelling spectroscopy is employed as a non-invasive probe to produce two-dimensional images of the probability density of an electron confined in a quantum dot. The images reveal clearly the elliptical symmetry of the ground state and the characteristic lobes of the higher energy states of the dots. We use the technique to compare the symmetry properties of the electron wavefunctions in QDs grown on (100)- and (311)B-oriented GaAs substrates.

Magneto-Tunnelling Spectroscopy for Spatial Mapping of Orbital Wavefunctions of the Ground and Excited Electronic States in Self-Assembled Quantum Dots

We present an experimental study of electron wavefunctions in InAs/GaAs self-assembled quantum dots (QDs). Magneto-tunnelling spectroscopy is employed as a non-invasive probe to produce two-dimensional images of the probability density of an electron confined in a quantum dot. The images reveal clearly the elliptical symmetry of the ground state and the characteristic lobes of the higher energy states of the dots. We use the technique to compare the symmetry properties of the electron wavefunctions in QDs grown on (100)- and (311)B-oriented GaAs substrates.

Real and spurious solutions of the8×8k⋅p model for nanostructures

Quantum dot wave functions are constructed in the $8\ifmmode\times\else\texttimes\fi{}8$ k\ensuremath{\cdot}p model from three bulk states: ${k}_{1},{k}_{2},$ and ${k}_{3}.$ We found that the $8\ifmmode\times\else\texttimes\fi{}8$ $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ ${k}_{2}$ bulk state (far from $\ensuremath{\Gamma},$ belonging to the electon-light hole bands) does not exist in the more realistic atomistic pseudopotential calculation. As a result, $8\ifmmode\times\else\texttimes\fi{}8$ k\ensuremath{\cdot}p nanostructure solutions which critically depend on this ${k}_{2}$ bulk state are spurious. These include the $8\ifmmode\times\else\texttimes\fi{}8$ k\ensuremath{\cdot}p quantum dot band gap ``intrinsic'' surface states and oscillating hole states. On the other hand, if the contribution of this ${k}_{2}$ state is small and decays with increasing nanostructure size, the corresponding nanostructure state is real.

Magnetotransport theory in quantum dots: 3D-0D and 2D-0D tunneling and angular momentum selection rules

A study of magnetotransport through quantum dots is presented. The model allows one to analyze tunneling both from bulk-like contacts and from 2D accumulation layers. The fine features in the $I\ensuremath{-}V$ characteristics due to the quantum dot states are known to be shifted to different voltages depending upon the value of the magnetic field. While this effect is also well reproduced by our calculations, in this work we concentrate on the amplitude of each current resonance as a function of the magnetic field. Such amplitudes show oscillations reflecting the variation of the density of states at the Fermi energy in the emitter. Furthermore the amplitude increases as a function of the magnetic field for certain features while it decreases for others. In particular, we demonstrate that the behavior of the amplitude of the current resonances is linked to the value of the angular momentum of each dot level through which tunneling occurs. We show that a selection rule on the angular momentum must be satisfied. As a consequence, tunneling through specific dot states is strongly suppressed and sometimes prohibited altogether by the presence of the magnetic field. This will allow to extract from the experimental curves detailed information on the nature of the quantum-dot wave functions involved in the electronic transport. Furthermore, when tunneling occurs from a two-dimensional accumulation layer to the quantum dot, the presence of a magnetic field hugely increases the strength of some resonant features. This effect is predicted by our model and, to the best of our knowledge, has never been observed.

Magneto-tunnelling spectroscopy of single self-assembled InAs quantum dots in AlAs

We observe the spin splitting of a single InAs quantum dot using magneto-tunnelling spectroscopy. The current–voltage characteristics at low temperature are dominated by a Fermi edge singularity, caused by electron interaction effects. We obtain a value for the g-factor (=0.82±0.09) for the quantum dot, with magnetic field applied in the plane of the dot. The magnetic field dependence of the amplitude of the tunnel current provides us with an estimate of the size of the quantum dot wave function (9 nm).

Exact Diagonal Calculations of Coulomb Oscillations in Quantum Dots

Transport properties through a quantum dot are examined based on exact diagonal calculations of many-body states, when the Coulomb interaction energy is comparable with one-electron level spacings. The peak positions of Coulomb oscillation show an atomic-like shell structure of one-electron levels, in agreement with recent experimental results. Some peaks of the conductance increase in height with increasing temperature. This anomalous temperature dependence reflects a level spacing as small as 1K and total spin of the ground state. The transport properties through coupled two dots are also investigated. We show that the correlation effect influences the peak heights of the conductance. These phenomena exemplify the observation of many-body wavefunctions in quantum dots, by the Coulomb oscillation.

Statistics of fluctuations of wave functions of chaotic electrons in a quantum dot in an arbitrary magnetic field.

Using the supersymmetry technique we calculate the distribution of local amplitudes of electron wave functions in quantum dots in the regime of chaotic motion. The exact formula for an arbitrary magnetic field is obtained from first principles; this provides the possibility of describing the crossover between the orthogonal and unitary ensembles. The distribution function of chaotic electron waves can be the basis for a calculation of the resonance conductance distribution function.