Elliptical Quantum Dots Research Articles

Impact of competing energy scales on the shell-filling sequence in elliptic bilayer graphene quantum dots

Impact of competing energy scales on the shell-filling sequence in elliptic bilayer graphene quantum dots

Hofstadter-like spectrum and magnetization of artificial graphene constructed with cylindrical and elliptical quantum dots

A comparative study of the electronic and magnetic properties of quasi-two-dimensional electrons in an artificial graphene-like superlattice composed of circular and elliptical quantum dots is presented. A complete orthonormal set of basis functions has been implemented for calculation of the energy dispersions, Hofstadter spectra, density of states and orbital magnetization of the considered systems. Our calculations indicate a topological change in the miniband structure due to the ellipticity of the quantum dots, and non-trivial modifications of the electron energy dispersion surfaces with the change of the magnetic flux per unite cell. The ellipticity of the quantum dots leads to an opening of a gap and considerable modifications of the Hofstadter spectrum. The orbital magnetization is shown to reveal significant oscillations with the change of the magnetic flux. The ellipticity of quantum dots has a qualitative impact on the dependencies of the magnetization on both the magnetic flux and the temperature.

Molecular Collapse States in Graphene/WSe_{2} Heterostructure Quantum Dots.

In relativistic physics, both atomic collapse in a heavy nucleus and Hawking radiation in a black hole are predicted to occur through the Klein tunneling process that couples particles and antiparticles. Recently, atomic collapse states (ACSs) were explicitly realized in graphene because of its relativistic Dirac excitation with a large "fine structure constant." However, the essential role of the Klein tunneling in the ACSs remains elusive in experiment. Here we systematically study the quasibound states in elliptical graphene quantum dots (GQDs) and two coupled circular GQDs. Bonding and antibonding molecular collapse states formed by two coupled ACSs are observed in both systems. Our experiments supported by theoretical calculations indicate that the antibonding state of the ACSs will change into a Klein-tunneling-induced quasibound state revealing deep connection between the ACSs and the Klein tunneling.

Impurity photo-ionization cross section and stark shift of ground and two low-lying excited electron-states in a core/shell ellipsoidal quantum dot

A new investigation on photo-ionization cross section (PICS) of a donor impurity confined in a GaAs/AlGaAs core/shell elliptic quantum dots (CSEQDs) has been performed under electric field (EF) effect. By means of the finite element method (FEM), we have computed the binding energy (BE), oscillator strength Pif and PICS within the framework of the effective mass theory (EMT). Our numerical results reveal that the stark shift is greatly dependent on the strength of the EF, the degree of ellipticity β, and the states of electronic transitions. It can take positive or negative values depending on the situation. In addition, the photo-ionization describing the transition from the donor impurity ground-state (1simp) to one of the conduction sub-band states (1s0, 2s0, and 2p0) is affected by the shape of the quantum dots (QDs) and the EF. We demonstrated that varying internal and external parameters may control the photo-ionization cross-section. These characteristics can be exploited to fabricate optoelectronic devices like QD infrared photodetectors.

Metal–Organic Vapor‐Phase Epitaxy of Semipolar InGaN Quantum Dots Based on GaN V‐Shaped Pits

Semipolar {101} InGaN quantum dots (QDs) formed on GaN V‐shaped pits by metal–organic vapor‐phase epitaxy (MOVPE) with a growth interruption method are reported. The 3D GaN V‐pit structures are directly grown on a patterned sapphire substrate (PSS). By adjusting the pattern arrangement direction on the substrate, it is observed in the scanning electron microscopy (SEM) image that elliptical QDs are formed on the {101} semipolar sidewalls of the V‐pits with a density of about 5 × 1010 cm−2. The emission wavelength of semipolar InGaN QDs is confirmed by cathodoluminescence (CL). The gradient distribution of In composition and QD size are observed along the sidewall of the V‐pits. On this basis, a three‐period semipolar InGaN QD sample is prepared. For the temperature‐dependent photoluminescence (TDPL) test, the prominent peak of the sample shows a blueshift with the increase in temperature and reaches the green band (≈523 nm) at room temperature (RT). According to time‐resolved photoluminescence (TRPL) decay curves, a carrier lifetime of 329.3 ps fit by the stretched exponential model is obtained at RT. Compared with c‐plane QDs with the same growth method, the semipolar QDs have a shorter radiative recombination lifetime due to suppressed polarization electric field.

Comparison of bound magneto-polaron in circular, elliptical, and triangular quantum dot qubit

In the present work, we consider an electron which is strongly coupled to the LO-phonon in circular, elliptical, and triangular quantum dots with Coulomb impurity. The eigenenergies and eigenfunctions of the ground and the first-excited states of the electron are obtained under magnetic and electric fields by using the Pekar variational method. We have also obtained the Shannon entropy and the electron probability density. This system can be applied as a two-level qubit. The entropy shows the oscillatory periodic evolution as function of the time due to the form of the confinement. It is seen that entropy has an arrangement periodic behavior for the higher symmetry (circular quantum dot).

Determination of the Eigenfunction’s and Eigenvalue’s of Quantum dots by FDTD

In this Article, we consider quantum dots with different structures and solve the Schrodinger equations for them by finite difference time-domain method and obtain the Eigenfunction’s and the Eigenvalue’s of these points.The FDTD method have an analysis that demonstrates the high accuracy of this method for solving quantum equations.The FDTD method is a suitable method for simulating electromagnetic phenomena, in this Article we present a simple formulation for the Schrodinger equation in FDTD. In fact, we get help from the idea of FDTD and solve quantum equations. The most important structures we have simulated with this method are cubic quantum dot, spherical quantum dot, elliptical quantum dot and partial truncate-shaped quantum dots on the wetting layer. It is very difficult to solve the Schrodinger equation analytically for these structures, but by using the numerical method we obtain the Eigenfunction’s and Eigenvalue’s in a simpler way.

Enhancement of surface plasmon resonances on the nonlinear optical properties in an elliptical quantum dot

In this paper, the nonlinear optical properties in an elliptical semiconductor quantum dot (SQD) have been calculated theoretically. A control laser field is applied to induced dipole moments in a metallic nanoparticle (MNP) and SQD, and they interact with each other through dipole–dipole interaction. By using the effective mass approximation, we can gain the eigenstates and eigenenergies of the MNP and SQD, respectively. And using the compact density matrix method, we can get the analytical expressions of the third-harmonic generation (THG), optical absorption coefficients (OA), and refractive index changes (RICs). It is found that the enhancement of the nonlinear optical properties is distinct when the MNP is close to the SQD. At the same time, these properties are also decreased by changing the radius of the MNP from 1 to 2 nm.

Effects of hydrogenic impurity and external fields on the optical absorption in a ring-shaped elliptical quantum dot

In this work, the effects of the hydrogenic impurity, electric and magnetic fields on the optical absorption of a typical GaAs/AlGaAs ring-shaped elliptical quantum dot are investigated. Energy eigenvalues and wave functions are calculated using the three-dimensional finite element method, and optical absorption is obtained using the density matrix approach. For the impurity located at the center of the quantum dot, results show that the optical absorption increases (decreases) with increasing electric (magnetic) field. Results also indicate that the off-center hydrogenic impurity considerably reduces the optical absorption.

Effects of anisotropy on the optical rectification of a disk-like quantum dot with donor impurity in external electric and magnetic fields

Based on the compact density matrix formalism and the effective mass approximation, optical rectification of a disk-like quantum dot in the presence of impurity has been studied, in this work. The effects of applied magnetics and electric fields and its direction on the optical rectification of an elliptic anisotropic quantum dot are analyzed in details. Our results show that the optical rectification is strongly affected by the anisotropy degree and the direction of the electric field. Also, we found that the binding energies of on-center impurity can be tuned with direction of electric field and anisotropy degree.

Rashba and Dresselhaus spin-orbit interactions effects on electronic features of a two dimensional elliptic quantum dot

In this paper, electronic structure of a two dimensional elliptic quantum dot under the influence of external electric and magnetic fields are studied in the presence of Rashba and Dresselhaus spin-orbit interactions. This investigation is done computationally and to do this, at first, the effective Hamiltonian of the system by considering the spin-orbit coupling is demonstrated in the presence of applied electric and magnetic fields and afterwards the Schrödinger equation is solved using the finite difference approach. Utilizing finite element method, eigenvalues and eigenstates of the system are calculated and the effect of the external fields, the size of the dot as well as the strength of Rashba spin-orbit interaction are studied. Our results indicate that, Spin-orbit interactions, external fields and the dot size have a great influence on the electronic structure of the system.

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

We consider a droplet of electrons confined within an external harmonic potential well of elliptical or ellipsoidal shape, a geometry commonly encountered in work with semiconductor quantum dots and other nanoscale or mesoscale structures. For droplet sizes exceeding the effective Bohr radius, the dominant contribution to average system parameters in the Thomas–Fermi approximation comes from the potential energy terms, which allows us to derive expressions describing the electron droplet’s shape and dimensions, its density, total and capacitive energy, and chemical potential. The analytical results are in very good agreement with experimental data and numerical calculations, and make it possible to follow the dependence of the properties of the system on its parameters (the total number of electrons, the axial ratios and curvatures of the confinement potential, and the dielectric constant of the material). An interesting feature is that the eccentricity of the electron droplet is not the same as that of its confining potential well.

Elliptical quantum dots as on-demand single photons sources with deterministic polarization states

In quantum information, control of the single photon's polarization is essential. Here, we demonstrate single photon generation in a pre-programmed and deterministic polarization state, on a chip-scale platform, utilizing site-controlled elliptical quantum dots (QDs) synthesized by a top-down approach. The polarization from the QD emission is found to be linear with a high degree of linear polarization and parallel to the long axis of the ellipse. Single photon emission with orthogonal polarizations is achieved, and the dependence of the degree of linear polarization on the QD geometry is analyzed.

Influence of applied electric fields on the electron-related second and third-order nonlinear optical responses in two dimensional elliptic quantum dots

The coefficients of the second-order nonlinear optical rectification and the generation of second and third harmonics, related to electron energy transitions in a two-dimensional elliptical quantum dot are calculated. The conduction band states are obtained using the finite element method to numerically solve the effective mass Schrödinger differential equation in the parabolic approximation, including the influence of an externally applied static electric field. It comes about that the geometry of the ellipse has a strong influence on the optical response, being the large eccentricity case the more favorable one. Furthermore, it is shown that the application of an electric field is of most importance for achieving well-resolved higher harmonics signals.

Polarization anisotropy of exciton in self-assembled elliptical InP/InGaP quantum dots

Optical anisotropy of self-assembled elliptical InP quantum dots has been investigated in terms of the polarization dependence of excitons. Although large size inhomogeneity is present, two kinds of characteristic quantum dots, which are classified into large and small quantum dots, were found in terms of the polarization anisotropy. We have confirmed that the large quantum dots are more pronounced in the polarization anisotropy, where the degree of linear polarization for the large quantum dots is significantly larger (∼60%) than that for the small ones (∼36%). The effective shape of quantum dots is also estimated by using the size dependence of oscillator strength, which is in agreement with the AFM image. We also suggest that the anisotropy of exciton oscillator strength can be modified via the dipole–dipole interaction between nearest exciton dipoles.

Wave functions of elliptical quantum dots in a magnetic field

We use the variational principle to obtain the wave functions of elliptical quantum dots under the influence of an external magnetic field. For the first excited states, whose wave functions have recently been mapped experimentally, we find a simple expression, based on a linear combination of the wave functions in the absence of a magnetic field. The results illustrate how a magnetic field breaks the x-y symmetry and mixes the corresponding eigenstates. The obtained eigenenergies agree well with those obtained by more involved analytical and numerical methods.

Nonadiabatic electron dynamics of single-electron transport in a perpendicular magnetic field

We present results of our investigation into the nonadiabatic electron dynamics of a moving quantum dot assisted by surface acoustic waves (SAWs) in a perpendicular magnetic field. The measurements show the evolution of a quantized acoustoelectric current in a modulated external field, which provides direct information of the energy spectrum and the occupation of the SAW-induced elliptical dynamical quantum dot. By comparing the magnetic field dependence of the spectrum with that of a somewhat symmetric circular dot, we find the appearance of nonadiabatic excitations at low magnetic fields resulting from the anisotropy of the dot. We also detect the transitions between different quantum states of the elliptical dot, achieved by exploiting the interference of two phase-tuned SAWs. Our results demonstrate that the quantum states in an asymmetric dot are fragile and extremely sensitive to their environment.

Electronic quantum trajectories in a quantum dot

This article gives a quantum‐trajectory demonstration of the observed electric, magnetic, and thermal effects on a quantum dot with circular or elliptic shape. By applying quantum trajectory method to a quantum dot, we reveal the quantum‐mechanical meanings of the classical concepts of backscattering and commensurability, which were used in the literature to explain the peak locations of the magnetoresistance curve. Under the quantum commensurability condition, electronic quantum trajectories in a circular quantum dot are shown to be stationary like a standing wave, whose presence increases the electrical resistance. A hidden quantum effect called magnetic stagnation is discovered and shown to be the main cause of the observed jumps of the magnetoresistance curve. Quantum trajectories in an elliptic quantum dot are found to be chaotic and an index of chaos called Lyapunov exponent is proposed to measure the irregularity of the various quantum trajectories. It is shown that the response of the Lyapunov exponent to the applied magnetic field captures the main features of the experimental magnetoresistance curve. © 2014 Wiley Periodicals, Inc.

Multipole-based modal analysis of gate-defined quantum dots in graphene

A new numerical method based on the multipoles of the Dirac equation is presented for rigorous and fast analysis of electron scattering from gate-defined structures in graphene. The new method is used to study the strongly bound states and the weakly bound states of a circular quantum dot. The accuracy of the obtained results is then verified by the T-matrix method. Furthermore, we characterize the resonances of elliptical gate-defined quantum dots and compare these resonances with the strongly bound states of circular dots. The effects of coupling between two quantum dots are also investigated.

Atomistic theoretical study of electronic and polarization properties of single and vertically stacked elliptical InAs quantum dots

The demonstration of isotropic polarization response from semiconductor quantum dots (QDs) is a crucial step towards the design of several optoelectronic technologies. Among many parameters that impact the degree of polarization (DOP${}_{[\stackrel{P\vec}{n}]}$) of a QD system, the shape asymmetry is a critical factor. We perform multi-million-atom simulations to study the impact of the elliptical shapes on the electronic and polarization properties of single and vertically stacked InAs QDs. The comparison between a low aspect ratio (AR) and a high AR QD reveals that the electronic and the polarization properties strongly depend on the AR of the QD; the elongation of a tall QD allows tuning of the DOP${}_{[\stackrel{P\vec}{n}]}$ over a much wider range. We then extend our analysis to an experimentally reported vertical stack of nine QDs (9-VSQDs) that has shown significant potential to achieve isotropic polarization properties. We analyze the contribution from the shape asymmetry in the large, experimentally measured, in-plane polarization anisotropy. Our analysis shows that the orientation of the base elongation controls the sign of the DOP${}_{[\stackrel{P\vec}{n}]}$; however, the magnitude of the base elongation has only a very little impact on the magnitude of the DOP${}_{[\stackrel{P\vec}{n}]}$. We further predict that the elliptical shape of the 9-VSQDs can only tune either DOP${}_{[110]}$ or DOP${}_{[\overline{1}10]}$ for the isotropic response. Our model results, in agreement with the TEM findings, suggest that the experimentally grown 9-VSQDs has either a circular or a slightly [$\overline{1}$10] elongated base. Overall, the detailed investigation of DOP${}_{[\stackrel{P\vec}{n}]}$ as a function of the QD shape asymmetry provides a theoretical guidance for the continuing experimental efforts to achieve tailored polarization properties from QD nanostructures for the design of optical devices.