Spontaneous spin polarization and electron localization in constrained geometries: The Wigner transition in nanowires

Abstract

The Wigner transition in a jellium model of cylindrical nanowires has been investigated by density-functional computations using the local spin-density approximation. A wide range of background densities ${\ensuremath{\rho}}_{b}$ has been explored from the nearly ideal metallic regime $({r}_{s}={[3/4\ensuremath{\pi}{\ensuremath{\rho}}_{b}]}^{1/3}=1)$ to the high correlation limit $({r}_{s}=100)$. Computations have been performed using an unconstrained plane wave expansion for the Kohn--Sham orbitals and a large simulation cell with up to 480 electrons. The electron and spin distributions retain the cylindrical symmetry of the Hamiltonian at high density, while electron localization and spin polarization arise nearly simultaneously in low-density wires $({r}_{s}\ensuremath{\sim}30)$. At sufficiently low density $({r}_{s}\ensuremath{\ge}40)$, the ground-state electron distribution is the superposition of well defined and nearly disjoint droplets, whose charge and spin densities integrate almost exactly to one electron and $1/2{\ensuremath{\mu}}_{B}$, respectively. Droplets are arranged on radial shells and define a distorted lattice whose structure is intermediate between bcc and fcc. Dislocations and grain boundaries are apparent in the droplets' configuration found by our simulations. Our computations aim at modeling the behavior of experimental low-carried density systems made of lightly doped semiconductor nanostructures or conducting polymers.