arXiv subjects
Publications and source records attributed to Augusto Gonzalez.
A set of theoretical results on infrared absorption and inelastic (Raman) scattering of light in semiconductor quantum dots is reviewed. When it is possible, qualitative comparisons with recent experimental results are presented.
The anharmonicity of a magnetic atomic trap at long distances from its center (forty times the radius of the first atomic orbit along the elongated axis, i.e. hundreds of microns) is shown to increase up to 45 % the temperature for Bose-Einstein condensation. This effect is perhaps small in the traditional traps, but should certainly be taken into account in magnetic microtraps, which characteristic dimensions are of order 1 mm.
A consistent semiquantitative theoretical analysis of electronic Raman scattering from many-electron quantum dots under resonance excitation conditions has been performed. The theory is based on random-phase-approximation-like wave functions, with the Coulomb interactions treated exactly, and hole valence-band mixing accounted for within the Kohn-Luttinger Hamiltonian framework. The widths of intermediate and final states in the scattering process, although treated phenomenologically, play a significant role in the calculations, particularly for well above band gap excitation. The calculated polarized and unpolarized Raman spectra reveal a great complexity of features and details when the incident light energy is swept from below, through, and above the quantum dot band gap. Incoming and outgoing resonances dramatically modify the Raman intensities of the single particle, charge density, and spin density excitations. The theoretical results are presented in detail and discussed with regard to experimental observations.
We report calculations of oscillator strengths for the far infrared absorption of light by the excitonic complexes Xn- (the excess charge, n, ranging from one to four) confined in quantum dots. The magnetic field is varied in an interval which corresponds to ``filling factors'' between 2 and 3/5. Electron-hole interaction effects are seen in the deviations of the peak positions from the Kohn lines, and in the spreading of the oscillator strengths over a few final states. Transition densities are used as an additional tool to characterize the absorption peaks.
A set of theoretical results [1-10] is reviewed, which concern calculations of energy spectra, density of energy levels, spin polarization, transport and optical properties (infrared absorption, luminescence) of semiconductor quantum dots and atomic traps. The studied systems contain a number of particles between 4 and 400, thus the calculation of their physical properties is a hard task. The analogy between these systems and the atomic nuclei is stressed and used throughout the paper. Common Nuclear Physics methods like Hartree-Fock and RPA schemes for finite systems, the BCS approach and the Lipkin-Nogami projection, and the Bethe-Goldstone equation were adapted to the present context. On the other hand, the Schrodinger equation was solved in basis with up to 40,000 functions by means of the Lanczos algorithm, and other methods like variational Monte Carlo estimations and two-point Pade approximants were also applied. Lastly, a stochastic projection of the BCS wave function was implemented.
A consistent calculation of resonant inelastic (Raman) scattering amplitudes for relatively large quantum dots, which takes account of valence-band mixing, discrete character of the spectrum in intermediate and final states, and interference effects, is presented. Raman peaks in charge and spin channels are compared with multipole strengths and with the density of energy levels in final states. A qualitative comparison with the available experimental results is given.
Exact diagonalization studies of the level density in a six-electron quantum dot under magnetic fields around 7 T (``filling factor'' around 1/2) are reported. In any spin-polarization channel, two regimes are visible in the dot excitation spectrum: one corresponding to interacting quasiparticles (i.e. composite fermions) for excitation energies below 0.4 meV, and a second one for energies above 0.4 meV, in which the level density (exponentially) increases at the same rate as in the non-interacting composite-fermion model.
Resonant inelastic (Raman) light scattering off neutral GaAs quantum dots which contain a mean number, N=42, of electron-hole pairs is computed. We find Raman amplitudes corresponding to strongly collective final states (charge-density excitations) of similar magnitude as the amplitudes related to weakly collective or single-particle excitations. As a function of the incident laser frequency or the magnetic field, they are rapidly varying amplitudes. It is argued that strong Raman peaks should come out in the spin-density channels, not related to valence-band mixing effects in the intermediate states.
A resonance behaviour of the far infrared absorption probability at a frequency \sim N^{1/4} is predicted for clusters of N electron-hole pairs (2\le N\le 110) confined in disk-shaped quantum dots. For radially symmetric dots, the absorption is dominated by a Giant Dipole Resonance, which accounts for more than 98 % of the energy-weighted photoabsorption sum rule.
Optical internal transitions relevant to ODR experiments are computed for the biexciton in a quantum dot in the strong confinement regime. Valence sub-band mixing effects are taken into account in second order pertubation theory. The transition probability from the ground state is concentrated in a few states with relatively high excitation energies. Level collissions with oscillator strength transfer are observed as the magnetic field is raised.
A BCS-like variational wave-function, which is exact in the infinite field limit, is used to study the interplay among Zeeman energies, lateral confinement and particle correlations induced by the Coulomb interactions in strongly pumped neutral quantum dots. Band mixing effects are partially incorporated by means of field-dependent masses and g-factors. The spin polarization and the magneto-luminescence are computed as functions of the number of electron-hole pairs present in the dot and the applied magnetic field.
One-electron tunneling through a quantum dot with a strong magnetic field in the direction of the current is studied. The linear magneto-conductance is computed for a model parabolic dot with seven electrons in the intermediate states and for different values of the magnetic field. It is shown that the dot density of states at low excitation energies can be extracted from a precise measurement of the conductance at the upper edge of the Coulomb blockade diamond. We parametrized the density of states with a single ``temperature'' parameter (in the so called ``constant temperature approximation''), and found that this parameter depends very weakly on the magnetic field.
The structure of E1 resonances is examined in a microscopic random phase approximation calculation for neutral, symmetric, closed shell, electron-hole systems in a quantum dot. The number of electron-hole pairs, N, is varied from 6 to 42. The ocurrence of small, but distinct, E1 peaks in the far infrared spectra located in the low energy tail of the giant dipole resonance and consisting of highly coherent electron-hole excitations is predicted. These pigmy resonances account for about 2 % of the dipole energy-weighted photoabsorption sum rule. A very weak dependence of the average pigmy resonance energy on the number of electron-hole pairs is found.
Interband absorption and luminescence of quasi-two-dimensional, circularly symmetric, N_e electron quantum dots are studied at high magnetic fields, 8<B<60 T, and low temperatures, T<<2 K. In the N_e=0 and 1 dots, the initial and final states of such processes are fixed, and thus the dependence on B of peak intensities is monotonic. For larger systems, ground state rearrangements with varying magnetic field lead to substantial modifications of the absorption and luminescence spectra. Collective effects are seen in the N_e=2 and 3 dots at "filling factors" 1/2, 1/3 and 1/5.
Confined excitonic complexes in two dimensions, consisting of N_e electrons and N_h holes, are studied by means of Bethe-Goldstone equations. Systems with up to twelve pairs, and asymmetric configurations with N_e \ne N_h are considered. The weak confinement regime gives indication of weak binding or even unbinding in the triexciton and the four-exciton system, and binding in the higher complexes.
Second order perturbation theory and a Lipkin-Nogami scheme combined with an exact Monte Carlo projection after variation are applied to compute the ground-state energy of $6\le N\le 210$ electron-hole pairs confined in a parabolic two-dimensional quantum dot. The energy shows nice scaling properties as N or the confinement strength is varied. A crossover from the high-density electron-hole phase to the BCS excitonic phase is found at a density which is roughly four times the close-packing density of excitons.
A new stochastic number projection method is proposed. The component of the BCS wave function corresponding to the right number of particles is obtained by means of a Metropolis algorithm in which the weight functions are constructed from the single-particle occupation probability. Either standard BCS or Lipkin-Nogami probability distributions can be used, thus the method is applicable for any pairing strength. The accuracy of the method is tested in the computation of pairing energies of model and real systems.
We study trapped systems of bosons at zero temperature in three and two dimensions. Conditions are fulfilled for the application of Gross-Pitaevskii theory with a positive scattering length. Series expansions for ground-state properties are obtained in both the noninteracting and the strong-coupling (Thomas-Fermi) limits. From these expansions, analytic estimates are presented in the form of two-point Padé approximants. We explicitly show the approximants for the total energy per particle and the chemical potential.