Effect of the long-range random potential on optical conductivity in a one-dimensional extended-Fermi-surface system

Abstract

We study the effect of the long-range random potential on optical conductivity in a one-dimensional interacting electron system with extended-Fermi surface. We apply Abelian bosonization to show that in one part of the momentum space the system has a metallic behavior with a gap in the spin sector, while in the other region of momentum space it behaves like a gapless Luttinger liquid (paramagnetic metallic phase). Consequently we consider the scattering of electrons with the long-range random potential (forward scattering disorder) in that region of momentum space, where the system is in gapless Luttinger liquid phase. The real part of the optical conductivity has no Drude peak for small frequency $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}0),$ but the Drude weight is nonzero and it has the doping dependence, while the imaginary part of the optical conductivity shows the usual $1/\ensuremath{\omega}$ behavior, like in the clean system, and it has no doping dependence. We explain the doping dependence with the help of one-dimensional exact density of states.