Density-functional theory of the electronic structure of Coulomb-confined quantum wires

We present self-consistent calculations of the electronic structure of quantum wires, based on the density-functional formalism of Kohn and Sham. The model studied is of quantum wires formed by charge transfer between a narrow ribbon of dopant and a two-dimensional GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As interface or quantum well. The physics of such quantum wires is found to be quite different from that of split-gate quantum wires. The inclusion of exchange-correlation effects in the theory is found to be essential for quantum wires of this type. For low linear electron densities, and if the dopant ribbon is close to the electron plane, all of the populated states in these quantum wires are strongly confined in the transverse direction, as in gated quantum wires. However, for higher electron densities and larger separations, the electronic structure is qualitatively different: The higher populated subbands are extremely weakly bound in the transverse direction and their wave functions extend far beyond the vicinity of the dopant ribbon. Experimental tests of these predictions using transport and capacitance measurements would be of interest.