Roughness scattering induced insulator-metal-insulator transition in a quantum wire

We have theoretically investigated the influence of interface roughness scattering on the low temperature mobility of electrons in quantum wires when electrons fill one or many subbands. We find the Drude conductance of the wire with length $\mathcal{L}$ first increases with increasing linear concentration of electrons $η$ and then decreases at larger concentrations. For small radius $R$ of the wire with length $\mathcal{L}$ the peak of the conductance $G_{max}$ is below $e^2/h$ so that electrons are localized. The height of this peak grows as a large power of $R$, so that at large $R$ the conductance $G_{max}$ exceeds $e^2/h$ and a window of concentrations with delocalized states (which we call the metallic window) opens around the peak. Thus, we predict an insulator-metal-insulator transition with increasing concentration for large enough $R$. Furthermore, we show that the metallic domain can be sub-divided into three smaller domains: 1) single-subband ballistic conductor, 2) many-subband ballistic conductor 3) diffusive metal, and use our results to estimate the conductance in these domains. Finally we estimate the critical value of $R_c(\mathcal{L})$ at which the metallic window opens for a given length $\mathcal{L}$ and find it to be in reasonable agreement with experiment.