Interaction-Induced Spin Polarization in Quantum Dots

The electronic states of lateral many electron quantum dots in high magnetic fields are analyzed in terms of energy and spin. In a regime with two Landau levels in the dot, several Coulomb blockade peaks are measured. A zig-zag pattern is found as it is known from the Fock-Darwin spectrum. However, only data from Landau level 0 show the typical spin-induced bimodality, whereas features from Landau level 1 cannot be explained with the Fock-Darwin picture. Instead, by including the interaction effects within spin-density-functional theory a good agreement between experiment and theory is obtained. The absence of bimodality on Landau level 1 is found to be due to strong spin polarization.Comment: 4 pages, 5 figure

Stability of the shell structure in 2D quantum dots

We study the effects of external impurities on the shell structure in semiconductor quantum dots by using a fast response-function method for solving the Kohn-Sham equations. We perform statistics of the addition energies up to 20 interacting electrons. The results show that the shell structure is generally preserved even if effects of high disorder are clear. The Coulomb interaction and the variation in ground-state spins have a strong effect on the addition-energy distributions, which in the noninteracting single-electron picture correspond to level statistics showing mixtures of Poisson and Wigner forms.Comment: 7 pages, 8 figures, submitted to Phys. Rev.

Geometric and impurity effects on quantum rings in magnetic fields

We investigate the effects of impurities and changing ring geometry on the energetics of quantum rings under different magnetic field strengths. We show that as the magnetic field and/or the electron number are/is increased, both the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become insensitive to whether the ring is circular or square in shape. This is in qualitative agreement with experiments. However, we also find that the Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities and can be completely obliterated by a high level of impurity density. In the many-electron calculations we use a recently developed fourth-order imaginary time projection algorithm that can exactly compute the density matrix of a free-electron in a uniform magnetic field.Comment: 8 pages, 7 figures, to appear in PR

Strictly correlated uniform electron droplets

We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching the tighter forms of the Lieb-Oxford bound recently proposed by Rasanen et al. [Phys. Rev. Lett. 102, 206406 (2009)]. The bound is satisfied in three-, two-, and one-dimensional droplets, and in the latter case it is reached exactly - regardless of the type of interaction considered. Our results provide useful reference data for delocalized strongly correlated systems, and they can be used in the development and testing of exchange-correlation density functionals in the framework of density-functional theory

Scale dependence of cosmological backreaction

Due to the non-commutation of spatial averaging and temporal evolution, inhomogeneities and anisotropies (cosmic structures) influence the evolution of the averaged Universe via the cosmological backreaction mechanism. We study the backreaction effect as a function of averaging scale in a perturbative approach up to higher orders. We calculate the hierarchy of the critical scales, at which 10% effects show up from averaging at different orders. The dominant contribution comes from the averaged spatial curvature, observable up to scales of 200 Mpc. The cosmic variance of the local Hubble rate is 10% (5%) for spherical regions of radius 40 (60) Mpc. We compare our result to the one from Newtonian cosmology and Hubble Space Telescope Key Project data.Comment: 6 pages, 2 figures; v3: substantial modifications, new figure

Rectangular quantum dots in high magnetic fields

We use density-functional methods to study the effects of an external magnetic field on two-dimensional quantum dots with a rectangular hard-wall confining potential. The increasing magnetic field leads to spin polarization and formation of a highly inhomogeneous maximum-density droplet at the predicted magnetic field strength. At higher fields, we find an oscillating behavior in the electron density and in the magnetization of the dot. We identify a rich variety of phenomena behind the periodicity and analyze the complicated many-electron dynamics, which is shown to be highly dependent on the shape of the quantum dot.Comment: 6 pages, 6 figures, submitted to Phys. Rev.

Exchange-energy functionals for finite two-dimensional systems

Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the exchange-hole potentials and exchange energies is found when compared with the exact-exchange reference data for the two-dimensional uniform electron gas and few-electron quantum dots, respectively. Thereby, this work significantly improves the availability of approximate density functionals for dealing with electrons in quasi-two-dimensional structures, which have various applications in semiconductor nanotechnology.Comment: 5 pages, 3 figure

On the violation of a local form of the Lieb-Oxford bound

In the framework of density-functional theory, several popular density functionals for exchange and correlation have been constructed to satisfy a local form of the Lieb-Oxford bound. In its original global expression, the bound represents a rigorous lower limit for the indirect Coulomb interaction energy. Here we employ exact-exchange calculations for the G2 test set to show that the local form of the bound is violated in an extensive range of both the dimensionless gradient and the average electron density. Hence, the results demonstrate the severity in the usage of the local form of the bound in functional development. On the other hand, our results suggest alternative ways to construct accurate density functionals for the exchange energy.Comment: (Submitted on 27 April 2012

Broken Symmetry in Density-Functional Theory: Analysis and Cure

We present a detailed analysis of the broken-symmetry mean-field solutions using a four-electron rectangular quantum dot as a model system. Comparisons of the density-functional theory predictions with the exact ones show that the symmetry breaking results from the single-configuration wave function used in the mean-field approach. As a general cure we present a scheme that systematically incorporates several configurations into the density-functional theory and restores the symmetry. This cure is easily applicable to any density-functional approach.Comment: 4 pages, 4 figures, submitted to PR

Interpreting eddy covariance data from heterogeneous Siberian tundra : land-cover-specific methane fluxes and spatial representativeness

The non-uniform spatial integration, an inherent feature of the eddy covariance (EC) method, creates a challenge for flux data interpretation in a heterogeneous environment, where the contribution of different land cover types varies with flow conditions, potentially resulting in biased estimates in comparison to the areally averaged fluxes and land cover attributes. We modelled flux footprints and characterized the spatial scale of our EC measurements in Tiksi, a tundra site in northern Siberia. We used leaf area index (LAI) and land cover class (LCC) data, derived from very-high-spatial-resolution satellite imagery and field surveys, and quantified the sensor location bias. We found that methane (CH4) fluxes varied strongly with wind direction (-0.09 to 0.59 mu gCH(4)m(-2) s(-1) on average) during summer 2014, reflecting the distribution of different LCCs. Other environmental factors had only a minor effect on short-term flux variations but influenced the seasonal trend. Using footprint weights of grouped LCCs as explanatory variables for the measured CH4 flux, we developed a multiple regression model to estimate LCC group-specific fluxes. This model showed that wet fen and graminoid tundra patches in locations with topography-enhanced wetness acted as strong sources (1.0 mu gCH(4) m(-2) s(-1) during the peak emission period), while mineral soils were significant sinks (-0.13 mu gCH(4) m(-2) s(-1)). To assess the representativeness of measurements, we upscaled the LCC group-specific fluxes to different spatial scales. Despite the landscape heterogeneity and rather poor representativeness of EC data with respect to the areally averaged LAI and coverage of some LCCs, the mean flux was close to the CH4 balance upscaled to an area of 6.3 km(2), with a location bias of 14 %. We recommend that EC site descriptions in a heterogeneous environment should be complemented with footprint-weighted high-resolution data on vegetation and other site characteristics.Peer reviewe