0000000000404985
AUTHOR
S. M. Reimann
Magic triangular and tetrahedral clusters
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.
Semiclassical Methods for the Description of Large Metal Clusters
One of the most fascinating aspects of clusters is that they can be made arbitrarily large and therefore provide links between the microscopic and the macroscopic world. It is challenging to study how their physical properties change when going from atoms and small molecules to the bulk limit of condensed matter. But also the models and mathematical tools themselves, which are used in order to tackle the many-body problem, are an object of study for the theoretician. In particular, the question of how far quantum-mechanics must be carried with increasing size and where classical pictures become appropriate is of great interest. In this spirit, we discuss here some semiclassical methods for …
Quantum dots in magnetic fields: Phase diagram and broken symmetry of the Chamon-Wen edge
Quantum dots in magnetic fields are studied within the current spin density functional formalism avoiding any spatial symmetry restrictions of the solutions. We find that the maximum density droplet reconstructs into states with broken internal symmetry: The Chamon-Wen edge co-exists with a modulation of the charge density along the edge. The phase boundaries between the polarization transition, the maximum density droplet and its reconstruction are in agreement with recent experimental results.
Hund's Rules and Spin Density Waves in Quantum Dots
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.
On the formation of Wigner molecules in small quantum dots
It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of Wigner molecules occurs at a density parameter $r_s\approx 4 a_B^*$ to the results of a straight-forward diagonalization of the Hamiltonian matrix.
Spin-density waves in superdeformed quantum dots
Abstract 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.
Deformations of quasi-two-dimensional electron gas 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…