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

We investigated theoretically 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 that the Drude conductance of the wire with length L first increases with increasing linear concentration of electrons eta and then decreases at larger concentrations. For small radius R of the wire with length 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 subdivided into three smaller domains: (1) single-subband ballistic conductor, (2) many-subband ballistic conductor, and (3) diffusive metal, and use our results to estimate the conductance in these domains. Finally, we estimate the critical value of R-c(L) at which the metallic window opens for a given length L and find it to be in reasonable agreement with experiment.