Electronic Properties of Thin Film Periodic Nanostructures

Density functional theory allows us calculate the Bloch functions and energy bands of an electron gas of density  confined to a thin-film periodic array parametrized by strip width a and spacing L. The Coulomb energy is included via the LDA and generalizations to spin-polarized media. We find the ground state to be a spin polarized antiferromagnet at, or near, one electron per unit cell ( = 1), and paramagnetic at  = 2. At  = 3, where, by analogy with Lieb's theorem for the Hubbard model one might expect a ferromagnetic ground state, we only find paramagnetism which we interpret as a failure of the tight-binding approximation to fit solutions of the wave equation. Interestingly, the procedures used to find a converged paramagnetic or antiferromagnetic ground state fail only for concentrations in the ranges 0.75 < | − 2| < 0.84. We attribute this instability to the presence of a new, possibly superconducting, phase outside the scope of the LDA at those concentrations.