Gaussian Confinement Research Articles

Effect of Rashba spin–orbit interaction on the ground state energy of a D0 centre in a GaAs quantum dot with Gaussian confinement

The ground state energy of a neutral hydrogenic donor impurity (D0) trapped in a three-dimensional GaAs quantum dot with Gaussian confinement is calculated in the presence of Rashba spin–orbit interaction. The effect of the spin–orbit interaction is incorporated by performing a unitary transformation and retaining terms up to quadratic in the spin–orbit interaction coefficient. For the resulting Hamiltonian, the Rayleigh-Ritz variational method is employed with a simple wave function within the framework of effective-mass envelope function theory to determine the ground state energy and the binding energy of the donor complex. The results show that the Rashba spin–orbit interaction reduces the total GS energy of the donor impurity.

The Binding Energy and Magnetic Susceptibility of an Off-Centre D0 Donor in the Presence of a Magnetic Field in a GaAs Quantum Dot with Gaussian Confinement: An Improved Treatment.

The binding energy and susceptibility of an off-centre neutral hydrogenic donor impurity (D0) trapped in a three-dimensional Gaussian quantum dot in the presence of an applied magnetic field are obtained by a variational method with an improved wave function. The results are obtained as a function of the quantum dot size, position of the impurity and the confinement strength.

Effective many-body parameters for atoms in nonseparable Gaussian optical potentials

We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and non-separability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold atom developments. We focus in particular on two potentials utilized in current ultracold atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our main numerical tools are discrete variable representations (DVRs), which combine many favorable features of spectral and grid-based methods, such as the computational advantage of exponential convergence and the convenience of an analytical representation of Hamiltonian matrix elements. Optimizations, such as symmetry adaptations and variational methods built on top of DVR methods, are presented and their convergence properties discussed. We also present a quantitative analysis of the degree of non-separability of eigenstates, borrowing ideas from the theory of matrix product states (MPSs), leading to both conceptual and computational gains. Beyond developing numerical methodologies, we present results for construction of optimally localized Wannier functions and tunneling and interaction matrix elements in optical lattices and tweezers relevant for constructing effective models for many-body physics.

Static polarizability of an atom confined in Gaussian potential

Optical properties like oscillator strength and polarizability have been calculated for a hydrogen atom under the effect of Gaussian potential and loose spherical confinement by solving the Schrodinger equation numerically. The finite basis set method based on B-polynomials has been successfully employed to calculate the energy spectrum of such systems. The effect of varying Gaussian confinement parameters on the energy spectrum, radial dipole matrix elements and optical properties has been investigated in detail. Dependence of static polarizability on the number of states chosen to represent the system has also been explored.

Energy and binding energy of donor impurity in quantum dot with Gaussian confinement

Using the method of the shifted 1/N expansion, we investigate the problem of hydrogenic-like donor impurity, located at the center of a spherical semiconductor quantum dot. We have calculated the energy eigenvalues for both ground and first excited sates under the assumption of Gaussian confining potential. The binding energies for three dimensional (3D) and two dimensional (2D) quantum dots are calculated. We show their dependence on dimensionality, dot radius and potential confinement. Our present numerical results show quantitative and qualitative very good agreement with those results obtained by diagonalization, Numerov’s integration, and Hartree–Fock methods.

The pinning effect in a polar semiconductor quantum dot with Gaussian confinement: A study using the improved Wigner–Brillouin perturbation theory

The effect of electron–phonon interaction on a few low-lying energy levels in a polar semiconductor quantum dot with Gaussian confinement is studied by using an improved Wigner–Brillouin perturbation theory (IWBPT). In the absence of the electron–phonon interaction, the electronic ground state plus one phonon state is degenerate with the first excited electronic state plus the zero-phonon state at some value of the confinement length. Similarly, the electronic ground state plus one phonon state is also degenerate with the second excited electronic state plus the zero-phonon state at a larger value of the confinement length. It is shown that the electron–phonon interaction lifts these degeneracies and as a result, the excited state energy levels bend downward and get pinned to the ground state plus one phonon state as the confinement frequency is increased. Our calculations are finally applied to GaAs and InSb quantum dots.

Two-Electron Resonances in Quasi-One Dimensional Quantum Dots with Gaussian Confinement

We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process. Employing the complex-coordinate rotation method, we determine the resonance widths and energies and discuss their dependence on the longitudinal confinement potential and the lateral radius of the quantum dot. The stability properties of the system are discussed.

A study of electric-field-induced second-harmonic generation in asymmetrical Gaussian potential quantum wells

Electric-field-induced second-harmonic generation in asymmetrical Gaussian potential quantum wells is investigated using the effective mass approximation employing the compact density matrix method and the iterative approach. Our results show that the absolute value, the real part and the imaginary part of second-harmonic generation are greatly affected by the height of the Gaussian potential quantum wells, the range of the Gaussian confinement potential and the applied electric field. The relationship between the absolute value and the imaginary part of second-harmonic generation together with the relationship between the absolute value and the real part of second-harmonic generation is studied. It is found that no matter how the height of the Gaussian potential quantum wells, the range of the Gaussian confinement potential and the applied electric field vary, the resonant peaks of the absolute value of second-harmonic generation do not originate from the imaginary part but from the real part.

Quantum confinement in nonadditive space with a spatially dependent effective mass for Si and Ge quantum wells

We calculate the effect of a spatially dependent effective mass (SPDEM) [adapted from Costa Filho et al. (2011)] on an electron and a hole confined in a quantum well (QW). In the work of Costa Filho et al., the translation operator is modified to include an inverse character length scale, γ, which defines the SPDEM. The introduction of γ means that translations are no longer additive. In nonadditive space, we choose a ‘skewed’ Gaussian confinement potential defined by the replacement x→γ−1ln(1+γx) in the usual Gaussian potential. Within the parabolic approximation γ is inversely related to the QW thickness and we obtain analytic solutions to our confinement Hamiltonian. Our calculation yields a reduced dispersion relation for the gap energy (EG) as a function of QW thickness, D:EG~D−1, compared to the effective mass approximation: EG~D−2. Additionally, nonadditive space contracts the position space metric thus increasing the occupied momentum space and reducing the effective mass, in agreement with the relation: mo⁎−1∝∂2E/∂k2. The change in the effective mass is shown to be a function of the confinement potential via a point canonical transformation. Our calculation agrees with experimental measurements of EG for Si and Ge QWs.

Effect of external magnetic field on the ground state properties of D− centres in a Gaussian quantum dot

The binding energies of a negatively charged hydrogenic donor ion (D−) trapped in a three-dimensional quantum dot with Gaussian confinement in the presence of an external magnetic field are obtained as a function of the quantum dot size and the confinement strength and also as a function of the magnetic field by a variational method with a simple wave function. A Jastrow-like factor is used to take care of the correlation effect. The results are obtained. The magnetic moment and susceptibility are also obtained for the donor complex. One of the most important objectives of this work is to study the effect of the magnetic field on the resultant dipole moment of a D− complex in a Gaussian QD. It is shown that the resultant dipole moment of a D− complex increases as the dot size increases and decreases as the magnetic field increases. The effect of the confinement strength on the resultant dipole moment is also investigated for different values of the magnetic field.

Effect of an external magnetic field on the binding energy, magnetic moment and susceptibility of an off-centre donor complex in a Gaussian quantum dot

The ground state energy and binding energy of an off-centre neutral hydrogenic donor impurity (D0) trapped in a three-dimensional quantum dot with Gaussian confinement are obtained by a variational method as a function of the position of the impurity and the magnetic field. The binding energy in the presence of a magnetic field is also calculated. The results show that the binding energy decreases as the impurity moves away from the origin.

Defect induced modifications in the optical, dielectric, and transport properties of hydrothermally prepared ZnS nanoparticles and nanorods

Zinc sulfide nanoparticles (particles size range 10–20 nm) and nanorods (particles size range 20–35 nm) were prepared through a hydrothermal method. The influence of surface defects and lattice strain on the optical, dielectric, and electrical transport properties was investigated. The spectral shifts and modification in bandgap are explained based on effective mass approximation model. Photoluminescence and ESR studies clearly showed the presence of large density of surface defects in the samples. The Raman spectra were thoroughly studied using the Gaussian confinement model. Dielectric studies using impedance and electric modulus spectroscopy showed enhanced grain boundary conductivity. Both nanoparticles and nanorods were found to exhibit Cole–Cole type dielectric relaxation. The enhanced ac electrical conductivities observed in both the nanostructures were successfully explained using the correlated barrier hopping model. Parameters like hopping time, barrier width, and defect densities were calculated.

Size and boundary effects on the diffusive behavior of elongated colloidal particles in a strongly confined dense dispersion

In very recent experimental work, diffusive motion of individual particles in a dense columnar phase of colloidal suspension of filamentous virus particles probed by means of fluorescence video microscopy [S. Naderi, E. Pouget, P. Ballesta, P. van der Schoot, M. P. Lettinga, and E. Grelet, Phys. Rev. Lett. 111, 037801 (2013)]. Rare events were observed in which the minority fluorescently labeled particles engage in sudden, jump-like motion along the director. The jump length distribution turned out to be biased towards a half and a full particle length. We suggest these events may be indicative of two types of particle motion, one in which particles overtake other particles in the same column and the other where a column re-equilibrates after a particle leaves a column either to enter into another column or into a void defect on the lattice. Our Brownian dynamics simulations of a quasi one-dimensional system of semi-flexible particles, subject to a Gaussian confinement potentials mimicking the effects of the self-consistent molecular field in the columnar phase, support this idea. We find that the frequency of overtaking depends on the linear fraction of particles and the steepness of the confining potential. The re-equilibration time of a column after a particle is removed from it is much shorter than the self-diffusion timescale. For the case of large system sizes and periodic boundary conditions, overtaking events do not present themselves as full-length jumps. Only if the boundary conditions are reflecting and the system is sufficiently small, full length jumps are observed in particle trajectories. The reason is that only then the amplitude of the background fluctuations is smaller than a particle length. Increasing the bending flexibility of the particles on the one hand enhances the ability of particles to overtake each other but on the other it enhances fluctuations that wash out full jumps in particle trajectories.

Ground state properties of a two-electron system in a three-dimensional GaAs quantum dot with Gaussian confinement in a magnetic field

The ground state properties of a system of two interacting electrons trapped in a three-dimensional GaAs quantum dot with Gaussian confinement under the influence of an externally applied magnetic field (B) are obtained using a variational method with a Chandrashekhr-like wave function containing only three variational parameters and involving a modified Jastrow correlation factor. The phase diagram for the two-electron singlet bound state is obtained in the parameter space of the confinement potential. The pair density function is calculated as a function of the electron-electron separation for a couple of magnetic fields and its peak positions are obtained to study the behaviour of the size of the electron pair as a function of the confinement length and the depth of the potential. The size of the electron pair is also obtained directly by calculating the expectation value of the electron-electron separation with respect to the system wave function. Finally, the behaviour of the ground state energy is studied as a function of the electron effective mass and the dielectric constant of a quantum dot.

Impurity effects in two-electron coupled quantum dots: entanglement modulation

We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulating the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting in two regimes: one of low entanglement and the other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that the magnitude of the oscillator strength of the system could provide an indication of the presence and characteristics of impurities and, therefore, the degree of entanglement.

Heat capacity and entropy of a GaAs quantum dot with Gaussian confinement

The heat capacity and entropy effects in a GaAs quantum dot with Gaussian confinement are calculated in the presence of a magnetic field and its interaction with the electron spin using the canonical ensemble approach. It is shown that the heat capacity shows a Schottky-like anomaly at a low temperature, while it approaches a saturation value 2k(B) as the temperature increases. As a function of the magnetic field, the heat capacity shows a maximum and then reduces to zero. Also the width of the maximum becomes wider with temperature. It is also shown that the heat capacity remains constant up to a certain value of the confinement length beyond which it displays a monotonic increase. However as a function of the confinement strength, though the heat capacity initially shows a significant drop, it remains constant thereafter. At low temperatures like T = 10 and 20 K, the entropy is found to decrease with increasing magnetic field, but at higher temperatures, it remains almost independent of the magnetic field. At high temperatures, entropy shows a monotonic increase with temperature, but at a sufficiently low temperature as the magnetic field decreases, the entropy is found to develop a shoulder which becomes more and more pronounced with decreasing magnetic field.

Ground state and binding energies of (D0), (D−) centres and resultant dipole moment of a (D−) centre in a GaAs quantum dot with Gaussian confinement

The binding energies of a neutral hydrogenic donor centre (D0) and a negatively charged hydrogenic ion (D−) trapped in a three-dimensional quantum dot with Gaussian confinement are obtained by a variational method with a very simple wave function containing a Jastrow-like factor. The results are obtained as a function of the quantum dot size and the confinement strength and are compared with those available in the literature. The resultant dipole moment of a (D−) complex is also calculated.

Persistent current through a semiconductor quantum dot with Gaussian confinement

Abstract The persistent diamagnetic current in a GaAs quantum dot with Gaussian confinement is calculated. It is shown that except at very low temperature or at high temperature, the persistent current increases with decreasing temperature. It is also shown that as a function of the dot size, the diamagnetic current exhibits a maximum at a certain confinement length. It is furthermore shown that for a shallow potential, the persistent current shows an interesting maximum structure as a function of the depth of the potential. At low temperature, the peak structure is pretty sharp but becomes broader and broader with increasing temperature.

Dia- and paramagnetism and total susceptibility of GaAs quantum dots with Gaussian confinement

The total magnetization and susceptibility arising from dia- and paramagnetic effects in a Gaussian quantum dot are calculated and their dependence on temperature (T) and magnetic field (B) are studied. The effect of spin on the magnetic susceptibility is also investigated. It is shown that at low temperature and low magnetic field the system in general shows paramagnetism and at high temperature and high magnetic field the diamagnetic state is found to be a preferred state. The paramagnetic–diamagnetic phase diagram is shown in the B–T plane.

MAGNETIC PROPERTIES OF SEMICONDUCTOR QUANTUM DOTS WITH GAUSSIAN CONFINEMENT

The magnetic properties such as magnetization and magnetic susceptibility are calculated for semiconductor quantum dots with Gaussian confinement. It is shown that the magnetization and magnetic susceptibility effects are quite significant for quantum dots with deep confining potential well and the parabolic potential is only a poor approximation of the Gaussian confinement.