Modified Luttinger model and quantum wires

Luttinger model reproduces well the plasmons energy spectrum of quantum wires but it gives a momenta distribution where the Fermi surface has disappeared. However, photoluminescence experiments from real quantum wires cleary show a sharp Fermi surface. To reconcile both aspects, the accurate plasmons spectrum and the existence of the Fermi surface, within the same exact formalism, we propose adding to the Luttinger Hamiltonian in its original form, a parameterized term that accounts for the scattering of plasmons by the impurities existing in real (dirty) wires. The Hamiltonian we obtain is still diagonalizable by bosonization, so that the plasmons excitation spectrum and the momenta distribution are exactly obtained in terms of the scattering strength parameter. It is explicitly shown that the added term causes the restoration of the Fermi surface. Moreover, we calculate the density correlations and demonstrate that they decay quickly enough as to give a liquid behavior instead of the crystalline state characteristic of the original Luttinger model with long-range interaction. We also consider the current-carrying state. In particular we study how the system conductivity varies with the interactions range. The new Hamiltonian is applied to describe a quantum wire of width δ viewed as a strictly one dimensional system of electrons for which the confinement effects are considered through an effective (width-dependent) pair potential.