The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and "exact" diagonalization methods. The spontaneous magnetization due to Hund's rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and the regime of strong magnetic fields in finite dot is examined. In addition, quasi-one-dimensional rings, deformed dots, and dot molecules are considered. (Less)

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Electronic structure of quantum dots

Nonlinear electron dynamics in metal clusters

Structural, electronic, and optical properties of the thiolate-protected Au38(SR)24 cluster are studied by density-functional theory computations (R = CH3 and R = C6H13) and by powder X-ray crystallography (R = C12H25). A low-energy structure which can be written as Au23@(Au(SR)2)3(Au2(SR)3)6 having a bi-icosahedral core and a chiral arrangement of the protecting gold−thiolate Au x (SR) y units yields an excellent match between the computed (for R = C6H13) and measured (for R = C12H25) powder X-ray diffraction function. We interpret in detail the electronic structure of the Au23 core by using a particle-in-a-cylinder model. Although the alkane thiolate ligands are achiral, the chiral structure of the ligand layer yields strong circular dichroism (CD) in the excitations below 2.2 eV for Au38(SCH3)24. Our calculated CD spectrum is in quantitative agreement with the previously measured low-energy CD signal of glutathione-protected Au38(SG)24. Our study demonstrates a new mechanism for the strong chiral respo...

Chirality and Electronic Structure of the Thiolate-Protected Au38 Nanocluster

The ground-state energy of the two-dimensional uniform electron gas has been calculated with a fixed-node diffusion Monte Carlo method, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We give a simple analytic representation of the correlation energy which fits our simulation data and includes several known high- and low-density limits. This parametrization provides a reliable local spin density energy functional for two-dimensional systems and an estimate for the spin susceptibility. Within the proposed model for the correlation energy, a weakly first-order polarization transition occurs shortly before Wigner crystallization as the density is lowered.

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Correlation energy and spin polarization in the 2D electron gas.

The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques.

Theory and application of explicitly correlated Gaussians

Spin density functional theory is used to calculate the ground state electronic structures of circular parabolic quantum dots. We find that such dots either have a spin configuration determined by Hund's rule or make a spin-density-wave-like state with zero total spin. The dependence of the spin-density-wave amplitudes on the density of the two-dimensional electron gas is studied.

Hund's Rules and Spin Density Waves in Quantum Dots

Using the methods of density functional theory and the jellium model we show that clusters with triangular [in two dimensions (2D)] or tetrahedral [in three dimensions (3D)] shapes have a strong shell structure and enhanced stability. Moreover, the shell closings correspond to the lowest magic numbers of a 2D and 3D harmonic oscillator and at the same time to the number of divalent atoms in close-packed triangles and tetrahedrons. Ab initio molecular dynamics simulations for Na and Mg clusters support the results of the jellium model.

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Magic triangular and tetrahedral clusters

Shell effects and Jahn-Teller deformations of quasi-two-dimensional jellium droplets are studied. Utilizing the ultimate jellium assumption, previously successfully used for three-dimensional systems, we calculate unrestricted shape relaxations and binding energies of the ground-state and the lowest isomers, using the methods of density-functional theory in the local spin-density approximation. Strong variations with particle number are found in the shape of the droplets. In particular, for certain magic electron numbers the shapes show triangular or circular symmetry, while for other electron numbers, more complicated symmetries are found. We finally show that from a more simple ``billiard'' model one gains a qualitative understanding of the mechanisms behind the shape deformations.

Deformations of quasi-two-dimensional electron gas clusters

Electronic shell structure and spin effects in deformed quantum dots are investigated using spin-density functional theory. We recently suggested (Koskinen et al., Phys. Rev. Lett. 79 (1997) 1389) that for circular dots, depending on the density of the two-dimensional electron gas and the electron number, a spin-density wave-like state can occur as a possible ground state. Here these studies are extended to deformed and superdeformed dots, which approach the limit of a finite quantum wire.

Spin-density waves in superdeformed quantum dots

Using the density functional Kohn-Sham method we show that the internal shapes of fermion clusters are nearly independent of the interparticle interactions. The odd-even staggering of the total energy of small nuclei and of sodium clusters are shown to be of the same origin. Tetrahedral deformations are predicted for 40, 70 and 112 atom sodium clusters. An alternative model for linear nuclei is suggested.

S. M. Reimann

Papers

Hund's Rules and Spin Density Waves in Quantum Dots

Magic triangular and tetrahedral clusters

Deformations of quasi-two-dimensional electron gas clusters

Spin-density waves in superdeformed quantum dots

Universal shapes of fermion clusters in the local density approximation