Melting of two-dimensional electron clusters in a magnetic field

The molecular dynamics method is applied to simulate the behavior of two-dimensional electron clusters of various shapes containing about 100 particles. The influence of a magnetic field on the effects of ordering and disordering (melting) in such clusters is studied. The field dependence of the rms displacements of particles in clusters is determined, and the trajectories of electron motion are found as functions of temperature and magnetic field. Ordering and disordering in clusters were fixed by the appearance of characteristic features in the rms displacements of electrons in the system. Hysteresis was observed in the field dependence of these displacements at a fixed temperature. The obtained data are compared with the results for root-mean-square displacements of electrons in a two-dimensional electronic infinite crystal. The qualitative agreement was found with these results; at the same time, the field dependence of root-mean-square displacements in an unbounded crystal is much weaker than in the clusters under study. The influence of the cluster shape on ordering transitions is studied, and it is found that the shape of a defect-free cluster does not affect the transition conditions. The distribution of electron velocities in clusters is studied for various magnetic fields. © V. E. Syvokon and S. S. Sokolov, 2023.