Wigner Molecules in Nanostructures

The charge density and the pair correlation function of interacting electrons with spin, confined within a quasi-one-dimensional ((quantum dot., are calculated by numerical diagonalization. The transition from a dense homogeneous charge distribution to a dilute Wigner-type electron arrangement is investigated. The influence of the long-range part of the Coulomb interaction is explicitly studied. When the interaction is exponentially screened the <mystallized. Wigner molecule is destroyed in favour of an inhomogeneous charge distribution similar to a charge density wave. Single charges dominate the electronic properties of submicron structures at low temperatures. Due to small capacitances the charging energy associated with the addition of one electron into a given structure can exceed the thermal energy. Two recently discovered important phenomena can be explained by single-electron charging effects: the Coulomb blockade of the d.c.-current through small tunnel junctions (l, 21, and the periodic oscillations of the conductance of quantum dots (3,4). In contrast to metallic systems, semiconductor nanostructures allow to reduce the number of electrons in a quantum dot by varying a gate voltage. Optical-absorption experiments were performed on quantum dots which contain only N = 2...4 electrons 151. For very low electron densities additional effects in the transport properties can be expected due to the increasing importance of the Coulomb interaction (6) since the electrons tend to ((crystallize. into an inhomogeneous ground state (7). Besides Coulomb effects, linear (81 and non-linear (91 transport experiments show fine structure in the current voltage characteristics that can be traced black to the granularity of the charge density distribution and to the lowest collective excitations (lo), respectively. Crystallized charge density distributions have been assumed recently ( 111 in the calculation of the transport properties of semiconductor nanostructures. We provide a microscopic justification of this assumption and analyse its range of validity. In this paper we consider a quasi-one-dimensional (1D) system containing a few interacting electrons with their spin degrees of freedom. We show that the charge density