Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by the scanning probe technique

• Published in: Journal of physics. Condensed matter Vol. 25; no. 33; p. 335801
• Main Authors: Wach, E, ebrowski, D P, Szafran, B
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 21.08.2013; Institute of Physics
• Subjects: Charge density; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Correlation; Droplets; Electron states and collective excitations in thin films, multilayers, quantum wells, mesoscopic and nanoscale systems; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Exact sciences and technology; Mapping; Mathematical models; Physics; Quantum dots; Superlattices; Two dimensional; Perturbation theory; Diagonalization; Quantum dots; Rectangular shape; Two-dimensional electron gas; Repulsive potential; Repulsion interaction; Wigner molecule; Charge density; Many electron system; Integral equations; Elliptic shape; Strongly correlated electron systems; Schroedinger equation; Droplets
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/25/33/335801

We perform a numerical simulation of the mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps as a function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are compared with the original ones. This study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limiting case. We concentrate on large quantum dots for which strong electron-electron correlations appear. For circular dots the correlations lead to the formation of Wigner molecules that in the presence of a tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for a repulsive tip potential and overestimated for an attractive tip. In lower symmetry quantum dots Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of a tip. These charge densities are well resolved by the mapping. These single-electron islands appear in the laboratory frame provided that the classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.