Classical two-dimensional atoms

Abstract

A classical two-dimensional system consisting of charged particles which are laterally confined by an artificial potential is investigated. This system is the classical analog of the well-known quantum dot problem. Using Monte Carlo techniques and molecular dynamics simulations we obtained the possible ordered structures and phase transitions for such a system. The particles group together in rings. A Mendeleev-type table for such classical atoms was obtained. When the size of the ‘classical atom’ is sufficiently large, the simple ring structure gradually disappears in the center and features of a Wigner lattice appear. The excitation spectrum and corresponding normal modes for these classical atoms are obtained. For atoms with a small number of charged particles the lowest excitation corresponds to an intershell rotation. Magic numbers are associated to clusters which are most stable against intershell rotation. For large systems the lowest excitation consists of a vortex/anti-vortex pair. The effect of a magnetic field on the excitation spectrum was calculated. We found that with increasing field the spectrum collapses into two branches. The upper branch corresponds to the cyclotron resonance energy, and the lower branch to the one of skipping orbits in a dot. Phase transitions in these ordered structures were investigated as a function of temperature. A two-step order-disorder transition was found: with increasing temperature first intershell rotation becomes possible and intershell rotational order disappears. At a second transition temperature intershell diffusion sets in. For large systems both transition temperatures coincide and equal the Wigner transition temperature.