# Microscopic origin of the Drude-Smith model

## TL;DR

This paper reexamines the Drude-Smith model's physical basis, deriving a modified formula grounded in diffusion and restoring currents, supported by Monte Carlo simulations, enhancing its theoretical foundation.

## Contribution

It introduces a physically motivated modification to the Drude-Smith model, replacing the backscattering explanation with a diffusive restoring current approach.

## Key findings

- Modified Drude-Smith model matches simulated conductivities without free parameters.
- The new model offers a more solid physical foundation for interpreting THz conductivities.
- Monte Carlo simulations validate the revised formula's accuracy.

## Abstract

The Drude-Smith model has been used extensively in fitting the THz conductivities of nanomaterials with carrier confinement on the mesoscopic scale. Here, we show that the conventional 'backscattering' explanation for the suppression of low-frequency conductivities in the Drude-Smith model is not consistent with a confined Drude gas of classical non-interacting electrons and we derive a modified Drude-Smith conductivity formula based on a diffusive restoring current. We perform Monte Carlo simulations of a model system and show that the modified Drude-Smith model reproduces the extracted conductivities without free parameters. This alternate route to the Drude-Smith model provides the popular formula with a more solid physical foundation and well-defined fit parameters.