2004/02/29 by M. M. Fogler
Physics and Astronomy · #Advanced Chemical Physics Studies #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.69.245321
published as Phys. Rev. B 69, 245321 (2004) · 15 pages, 7 figures
openalex publication_date 2004/06/25 · arxiv created 2004/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are investigated: an elongated metallic island, an antidot, and a constriction. In the first two cases complete closed-form analytical solutions are obtained, despite the absence of rotational or translational symmetries. These solutions govern the shape and size of large quantum dots, and also the size of the depletion regions and the density profiles around isolated antidots. For the constriction, an exact asymptotical formula for boundary shape is derived and arguments are given in favor of its universality. For the cases where the full analytical solution cannot be obtained, an approximate method is proposed as an alternative. Its accuracy is verified against numerical simulations in a periodic (checkerboard) geometry.