The Drude‐Smith Equation and Related Equations for the Frequency‐Dependent Electrical Conductivity of Materials: Insight from a Memory Function Formalism

• Published in: Chemphyschem Vol. 22; no. 16; pp. 1667 - 1674
• Main Authors: Chen, Wei‐Chen, Marcus, Rudolph A.
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 18.08.2021; John Wiley and Sons Inc
• Subjects: Backscattering; Computational fluid dynamics; conductivity; Current carriers; Drude equation; Drude-Smith equation; Electrical resistivity; Formalism; memory function terahertz region; Molecular dynamics
• ISSN: 1439-4235; 1439-7641; 1439-7641
• DOI: 10.1002/cphc.202100299

The Drude‐Smith equation is widely used for treating the frequency‐dependent electrical conductivity of materials in the terahertz region. An attractive feature is its sparsity of adjustable parameters. A significant improvement over Drude theory for these materials, the theory includes backscattering of the charge carriers. It has nevertheless been criticized, including by Smith himself, because of the arbitrariness of a step in the derivation. We recall a somewhat similar behavior of back scattering in fluids observed in molecular dynamics computations and discussed in terms of memory functions. We show how theories such as Drude‐Smith and Cocker et al. are examples of a broader class of theories by showing how they also arise as particular cases of a memory function formalism that divides the interactions into short and long range. Insight into the Drude‐Smith equation commonly used to treat terahertz electrical conductivity of solids and the role of backscattering is obtained using extensive computer‐based studies of a related quantity, the velocity autocorrelation function of fluids. The latter has been interpreted using a memory function formalism which is then used here to analyze and extend the Drude‐Smith equation.