Microscopic origin of the Drude-Smith model

Terahertz spectroscopy of nanomaterials is one of the most active areas of terahertz physics thanks to its ability to reveal charge-carrier confinement on length scales of tens to hundreds of nanometers. Structural confinement modifies the experimental complex conductivity, such that it is Drude-like at high frequencies but suppressed at low frequencies. This response is often described as a consequence of carrier backscattering off nanoparticle boundaries and modeled using the sometimes controversial Drude-Smith formula. In this paper, it is demonstrated that the terahertz conductivity of a structurally confined Drude gas of electrons is actually suppressed at low frequencies due to carrier confinement on the diffusion length scale and not due to backscattering. A new conductivity formula is derived based on diffusion that is found to be very similar to the Drude-Smith conductivity formula, thereby explaining many of the previous successes of the Drude-Smith model.