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We briefly report on calculated addition spectra for electrons in a circular quantum dot with perpendicular magnetic field. We compare our current density functional theory calculations with recent experiments by Tarucha et al. [PRL 77, 3613 (1996)]. We find a very good qualitative agreement of the structures and find an additional effect caused by Hund's first rule in magnetic field, which gives rise to new substructures not discussed in the paper by Tarucha.
We report on ground-state calculations based on current-spin density-functional theory for circular parabolic quantum dots. Hund's first rule, well-known from atomic physics, applies not only at zero magnetic field; analogous rules, related to the level occupancy near the Fermi energy, determine the spin configuration of the ground state in finite magnetic field. Consequently, the addition spectrum of the quantum dot exhibits a specific non-monotonous dependence on magnetic field. We discuss our results with focus on recent experiments which may already contain indications of this new feature.
We review ground-state properties and collective excitations of semiconductor quantum dots in a magnetic field obtained from current-spin density-functional theory. Due to exchange-correlation, a generalized Hund’s rule in magnetic field can be established which leads to spin alignment in partially occupied energy shells at the Fermi energy. This results, in distinct spin structures in single-electron addition spectra. Current-dependent exchange-correlation modifies the magnetic-field dependence of the ground state configuration and leads to deviations from plain spin-density calculations. Moreover it gives rise to spontaneous current textures at zero magnetic field. Collective excitation spectra, explicitly calculated for inelastic light scattering, exhibit novel features in their magnetic field dependence due to a finite ground-state spin density.
Magnetoresistance measurements and theoretical calculations for two-dimensional electron systems under a perpendicular magnetic field are presented which illuminate transport effects due to a periodic electrostatic potential modulation. We focus on features arising from the resolution of the magnetic miniband structure which are beyond the perturbative regime governed by the dispersion of Landau bands. Our non-perturbative quantum-mechanical calculations reveal that the dispersion of individual minibands is responsible for the complicated behaviour of the magnetoresistance in the regime of intermediate modulation strength. In particular, the interplay between miniband and scattering contributions to the conductivity leads to an almost structureless magnetoresistance in this regime followed by the formation of antidot peaks due to the miniband conductivity.
We present ground-state calculations for laterally coupled quantum dots containing 2, 4, and 8 electrons. As our emphasis is on spin effects our results are obtained by applying spin-density functional theory (SDFT). By varying the distance between the centers of the coupled quantum dots, the transition from weak to strong coupling situation is realized. For the 2-electron system we also apply the Heitler-London approximation and analytical concepts to check the reliability of SDFT calculations in this case. In addition we discuss the features of the Coulomb staircase of laterally coupled quantum dots in the weak and strong coupling regimes in comparison to that of a circular parabolic quantum dot.
Ground-state calculations based on current spin density-functional theory for circular parabolic quantum dots are presented which reveal interesting spin effects in dependence on an external magnetic field: Hund's first rule (well-known from atomic physics for zero magnetic field) is related to the level occupancy near the Fermi energy and determines the spin configuration of the ground state in finite magnetic field. Consequently, the addition spectrum of the quantum dot exhibits a specific non-monotonous dependence on magnetic field, which is visible in recent quantum transport experiments.
We present current-spin density-functional calculations for circular parabolic quantum dots in zero magnetic field. We find the possibility for broken time-reversal symmetry via exchange correlation with spontaneously induced orbital currents. For certain electron numbers, this results in new current textures which give rise to a finite magnetization even for ground states with vanishing total angular momentum.
We employ a self-consistent, dynamic spin-density functional concept beyond the dipole approximation in order to calculate the collective modes of few-electron quantum dots with partial spin polarization. Because of Hund's rule in a magnetic field the mode energies exhibit characteristic discontinuities in their magnetic-field dependence, which is a manifestation of ground-state transitions between different spin configurations. A finite ground-state spin density couples collective charge- and spin-density excitations. We predict their observability in state-of-the-art Raman experiments.
We study the energy-level statistics for electrons in a lateral two-dimensional superlattice in dependence on the strength of the modulation potential at a given perpendicular magnetic field. The interminiband statistics at some selected point in the magnetic Brillouin zone shows a transition from degenerate Landau levels to universal spectral correlations while the corresponding classical dynamics displays a crossover from regular cyclotron orbits to chaotic motion. In terms of the nearest-neighbor spacing distribution, we observe the occurrence of level repulsion for all nonzero modulation amplitudes, which indicates a discontinuous transition to universal fluctuations for the smallest level spacings when the rotational invariance of the system is broken by a finite superlattice potential. In order to test the universality of the transition on larger scales, we propose a random matrix model with one transition parameter for comparison. Confirmed by two different types of potential shapes, we detect an explicit influence of the potential shape on the level spacing distributions, which hence cannot be described by the one-parameter model. Using the spectral rigidity, however, universal long-range fluctuations in the regime of negligible Landau-level mixing are found, in agreement with our random matrix model.
