Dielectric response function for a quasi-one-dimensional semiconducting system

Abstract

We have obtained the dielectric response function for a quasi-one-dimensional electron gas (Q1D). In the static limit (ω=0), we find that the dielectric function has a logarithmic singularity as a function of wave vector when q=2kf when the electron gas is degenerate, but that this singularity no longer occurs when the electron gas is nondegenerate. This singularity is considered to be indicative of the Peierls transition which has been predicted to occur in a one-dimensional electron gas. As the radius of our quantum well wire goes to zero, the dielectric response function is found to diverge logarithmically. This divergence is independent of the degeneracy of the electron gas or the value of q or ω, but is indicative of the divergence of the one-dimensional Fourier transform of the Coulomb potential. We compare our results to other calculations of the dielectric function for one- and quasi-one-dimensional systems, and discuss the reasons for the differences in the various results. The momentum relaxation rates for scattering of carriers by background and remote ionized impurities in a quantum well wire are investigated.