Pencil-case structure in electron distribution of very thin film

The ground-state properties in a very thin film are investigated using the planar uniform jellium model as the positive charge background on the basis of the spin density functional theory treated within the local spin density approximation with the Perdew–Zunger type exchange-correlation energy. For a given electron density, the quasi-two-dimensional system undergoes a transition from a fluid to a one-dimensional electron-self-confined (1D ESC) state with an electron distribution of pencil-case structure, as the film thickness D is decreased. Even in metallic films, a 1D ESC state is always realized in the limit of small D.