Density functional theory of two-dimensional electronic structures in a magnetic field.

摘要

Most of the work done in the physics of two-dimensional structures is either limited by the size of the systems that are studied due to the use of exact diagonalization techniques which do not allow to go beyond structures with only few electrons, or by other methods which do not include exchange-correlation effects, or correlation effects only. There are instances in which these effects cannot be neglected. In order to fill this gap we decided to use a density functional approach, which proved to be reliable in other problems. In Chapter 3 I shall present original results on the study of the ground-state properties of quantum dots in the presence of a magnetic field of arbitrary strength obtained within a current-density functional approach. The results obtained agree very well with those obtained by means of exact diagonalization approaches. In the regime not accessible by the latter methods we show how important are exchange-correlation effects, and we also make an analysis of correlation effects, by comparison with Hartree-Fock results.; In Chapter 4 we address and study the density profile at the edge of a confined two-dimensional electron gas in the fractional quantum Hall regime. The strong correlation effects are accounted for in a density functional approach. I show that there exists a transition between two regimes as a function of the smoothness of the confining potential.; In Chapter 5, we study the magnetophonon dispersion relations of a two-dimensional Wigner crystal in the presence of a strong magnetic field, and of its shear modulus, that we derived within a density functional scheme, that therefore includes correlation effects, and has the advantage of being analytical.; In Chapter 6 I present a theory for the calculation of the pinning gap and magnetophonon spectrum of a disordered Wigner crystal. Its main feature resides in the inclusion in the pinning energy of the contribution arising from distortions of the crystal on all length scales.