Localization of electrons and formation of two-dimensional Wigner spin lattices in a special cylindrical semiconductor stripe

Abstract

We consider a two-dimensional (2D)electron gas residing on the surface of a cylinder of a given radius $R$ in the presence of a parabolic confinement along the axis of the cylinder. In this way the system of electrons forms a closed cylindrical stripe (wire). Using the local spin-density technique we first consider localization of electrons within of a potential barrier embedded in the wire. Barriers with sharp retangularlike features are populated in steps because of Coulomb blockade. The nature of a single bound state in a short soft barrier (quantum point contacts) at pinch-off is discussed in terms Coulomb blockade. For a shallow barrier-free wire we retrace the structural transitions at low electron densities from a single chain of localized states to double and triple chains (Wigner spin lattices). The present system is related to the model of a inhomogeneous quantum wire introduced recently by G\"u\ifmmode \mbox{\c{c}}\else \c{c}\fi{}l\"u et al. [Phys. Rev. B 80, 201302(R) (2009)]. An important aspect is, however, the present extension into higher electron densities as well as to the low-density regime and the formation of 2D Wigner microlattices.