Electronic Properties of Quasi-One-Dimensional Semiconductor Nanostructures: Plasmons and Exchange-Correlation Effects in Quantum Wires

We review the many-body exchange-correlation properties of electrons confined to the lowest sub-band of a quantum wire, including effects of impurity scattering. Without impurity scattering, the virtual excitations of arbitrarily low energy one-dimensional plasmons destroy the Fermi surface of the electrons, whereas the presence of impurity scattering damps out the low energy plasmons and restores the Fermi surface. The electron inelastic scattering rate r in the absence of scattering is zero below a critical wavevector kc corresponding to the plasmon emission threshold, above which r diverges as (k - kc )-1/2 for k -t kc. For typical wire widths and electron densities currently available, the calculated bandgap renormalisation is found to be on the order of 10-20 meV. We also calculate the finite-temperature inelastic scattering rates and mean free paths of electrons injected into a quantum wire containing a quasi-one-dimensional electron gas. We show that there is a very sharp increase in the electron scattering rate at the one-dimensional plasmon emission threshold. Based on these results, we suggest the possibility of a one-dimensional hot-electron device which possesses an I - V curve with a sharp onset of a large negative differential resistance. We also present a general method for obtaining expressions for the analytic continuation of finite-temperature self-energies which are suitable for use in numerical computations. In the case of the GW approximation for the self-energy, this method gives the finite-temperature generalisation of the zero-temperature 'line and pole' decomposition. This formalism is used to calculate the finite-temperature self-energy and bandgap renormalisation of electrons in the extreme quantum limit of a quantum wire. A brief review of the experimental and theoretical status of plasmons in quantum wire structures is given.