Phase lapses in scattering through multi-electron quantum dots: Mean-field and few-particle regimes

We show that the observed evolution of the transmission phase through multi-electron quantum dots with more than approximately ten electrons, which shows a universal (i.e., independent of N) as yet unexplained behavior, is consistent with an electrostatic model, where electron-electron interaction is described by a mean-field approach. Moreover, we perform exact calculations for an open 1D quantum dot and show that carrier correlations may give rise to a non-universal (i.e., N-dependent) behavior of the transmission phase, ensuing from Fano resonances, which is consistent with experiments with a few (N < 10) carriers. Our results suggest that in the universal regime the coherent transmission takes place through a single level while in the few-particle regime the correlated scattering state is determined by the number of bound particles.Comment: 14 pages, 3 figures, RevTex4 preprint format, to appear in Phys. Rev.

Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets

We compute the exact single-particle time-resolved dynamics of electronic Mach-Zehnder interferometers based on Landau edge-states transport, and assess the effect of the spatial localization of carriers on the interference pattern. The exact carrier dynamics is obtained by solving numerically the time-dependent Schroedinger equation with a suitable 2D potential profile reproducing the interferometer design. An external magnetic field, driving the system to the quantum Hall regime with filling factor one, is included. The injected carriers are represented by a superposition of edge states and their interference pattern reproduces the results of Y.Ji et al.[Nature 422, 415 (2003)]. By tuning the system towards different regimes, we find two additional features in the transmission spectra, both related to carrier localization, namely a damping of the Aharonov-Bohm oscillations with increasing difference in the arms length, and an increased mean transmission that we trace to the energy-dependent transmittance of quantum point contacts. Finally, we present an analytical model, also accounting for the finite spatial dispersion of the carriers, able to reproduce the above effects.Comment: two-columns, 12 pages, 9 figures; added 10 refs.; main text modified; corrected few typos; added 3 figures of Supplementary Dat

Landau levels, edge states and magneto-conductance in GaAs/AlGaAs core-shell nanowires

Magnetic states of the electron gas confined in modulation-doped core-shell nanowires are calculated for a transverse field of arbitrary strength and orientation. Magneto-conductance is predicted within the Landauer approach. The modeling takes fully into account the radial material modulation, the prismatic symmetry and the doping profile of realistic GaAs/AlGaAs devices within an envelope-function approach, and electron-electron interaction is included in a mean-field self-consistent approach. Calculations show that in the low free-carrier density regime, magnetic states can be described in terms of Landau levels and edge states, similar to planar two-dimensional electron gases in a Hall bar. However, at higher carrier density the dominating electron-electron interaction leads to a strongly inhomogeneous localization at the prismatic heterointerface. This gives rise to a complex band dispersion, with local minima at finite values of the longitudinal wave vector, and a region of negative magneto-resistance. The predicted marked anisotropy of the magneto-conductance with field direction is a direct probe of the inhomogeneous electron gas localization of the conductive channel induced by the prismatic geometry

Exact two-body quantum dynamics of an electron-hole pair in semiconductor coupled quantum wells: a time-dependent approach

We simulate the time-dependent coherent dynamics of a spatially indirect exciton (an electron-hole pair with the two particles confined in different layers) in a GaAs coupled quantum well system. We use a unitary wave-packet propagation method taking into account in full the four degrees of freedom of the two particles in a two-dimensional system, including both the long-range Coulomb attraction and arbitrary two-dimensional electrostatic potentials affecting the electron and/or the hole separately. The method has been implemented for massively parallel architectures to cope with the huge numerical problem, showing good scaling properties and allowing evolution for tens of picoseconds. We have investigated both transient time phenomena and asymptotic time transmission and reflection coefficients for potential profiles consisting of i) extended barriers and wells and ii) a single-slit geometry. We found clear signatures of the internal two-body dynamics, with transient phenomena in the picosecond time-scale which might be revealed by optical spectroscopy. Exact results have been compared with mean-field approaches which, neglecting dynamical correlations by construction, turn out to be inadequate to describe the electron-hole pair evolution in realistic experimental conditions.Comment: 12 two-column pages + 3 supplemental material pages, 9 figures, to appear on Phys.Rev.

Space- and time-dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures

We study the unitary propagation of a two-particle one-dimensional Schr\"odinger equation by means of the Split-Step Fourier method, to study the coherent evolution of a spatially indirect exciton (IX) in semiconductor heterostructures. The mutual Coulomb interaction of the electron-hole pair and the electrostatic potentials generated by external gates and acting on the two particles separately are taken into account exactly in the two-particle dynamics. As relevant examples, step/downhill and barrier/well potential profiles are considered. The space- and time-dependent evolution during the scattering event as well as the asymptotic time behavior are analyzed. For typical parameters of GaAs-based devices the transmission or reflection of the pair turns out to be a complex two-particle process, due to comparable and competing Coulomb, electrostatic and kinetic energy scales. Depending on the intensity and anisotropy of the scattering potentials, the quantum evolution may result in excitation of the IX internal degrees of freedom, dissociation of the pair, or transmission in small periodic IX wavepackets due to dwelling of one particle in the barrier region. We discuss the occurrence of each process in the full parameter space of the scattering potentials and the relevance of our results for current excitronic technologies.Comment: 28 pages, 10 figures, preprint forma

Symmetries in the collective excitations of an electron gas in core-shell nanowires

We study the collective excitations and inelastic light scattering cross-section of an electron gas confined in a GaAs/AlGaAs coaxial quantum well. These system can be engineered in a core-multi-shell nanowire and inherit the hexagonal symmetry of the underlying nanowire substrate. As a result, the electron gas forms both quasi 1D channels and quasi 2D channels at the quantum well bents and facets, respectively. Calculations are performed within the RPA and TDDFT approaches. We derive symmetry arguments which allow to enumerate and classify charge and spin excitations and determine whether excitations may survive to Landau damping. We also derive inelastic light scattering selection rules for different scattering geometries. Computational issues stemming from the need to use a symmetry compliant grid are also investigated systematically

Entanglement creation in semiconductor quantum dot charge qubit

We study theoretically the appearance of quantum correlations in two- and three-electron scattering in single and double dots. The key role played by transport resonances into entanglement formation between the single-particle states is shown. Both reflected and transmitted components of the scattered particle wavefunction are used to evaluate the quantum correlations between the incident carrier and the bound particle(s) in the dots. Our investigation provides a guideline for the analysis of decoherence effects due to the Coulomb scattering in semiconductor quantum dots structures.Comment: 8 pages, 5 figures, Proceedings of Quantum 2010:24-28, May, 2010 Torin

Promoting creative insubordination using Escape Games in mathematics

While the development of creativity, or creative thinking, in mathematics is considered important by many researchers, there are several difficulties in implementing creative tasks, especially before secondary school. Within the original context of a mathematical escape game, this paper reports two episodes exemplifying the difficulties met by sixth graders in abandoning stereotyped habits and acting with creative insubordination. While in the first episode, the puzzling task does not suffice to prompt creativity, in the second episode we show that an original solution may prompt unexpected mathematical contents. In conclusion, escape games could be useful to prompt creativity even in lower grades than it is now shown in the literature, but attention should be paid to the teacher’s role in sustaining such creative activities

Effect of the Coulomb interaction on the electron relaxation of weakly-confined quantum dot systems

We study acoustic-phonon-induced relaxation of charge excitations in single and tunnel-coupled quantum dots containing few confined interacting electrons. The Full Configuration Interaction approach is used to account for the electron-electron repulsion. Electron-phonon interaction is accounted for through both deformation potential and piezoelectric field mechanisms. We show that electronic correlations generally reduce intradot and interdot transition rates with respect to corresponding single-electron transitions, but this effect is lessened by external magnetic fields. On the other hand, piezoelectric field scattering is found to become the dominant relaxation mechanism as the number of confined electrons increases. Previous proposals to strongly suppress electron-phonon coupling in properly designed single-electron quantum dots are shown to hold also in multi-electron devices. Our results indicate that few-electron orbital degrees of freedom are more stable than single-electron ones.Comment: 20 pages (preprint format), 7 figures, submitted to Phys. Rev.

Magneto-photoluminescence in GaAs/AlAs core-multishell nanowires: a theoretical investigation

The magneto-photoluminescence in modulation doped core-multishell nanowires is predicted as a function of photo-excitation intensity in non-perturbative transverse magnetic fields. We use a self-consistent field approach within the effective mass approximation to determine the photoexcited electron and hole populations, including the complex composition and anisotropic geometry of the nano-material. The evolution of the photoluminescence is analyzed as a function of i) photo-excitation power, ii) magnetic field intensity, iii) type of doping, and iv) anisotropy with respect to field orientation.Comment: 11 pages, 11 figures, accepted for publication in Physical Review