We present a self-consistent Thomas-Fermi (TF) analysis of confined fermions with interactions in two dimensions. While the formalism may be developed for arbitrary forms of two-body interactions, we show that the TF model with logarithmic interactions is in fact an exactly solvable model. Furthermore, we show that the quantum corrections to the Thomas-Fermi energies reproduce the main features, namely the shell effects, seen in recent experiments.

• Received 31 May 2000

DOI:https://doi.org/10.1103/PhysRevB.62.10896