Derivation of the Drude conductivity from quantum kinetic equations

Kitamura, Hikaru

doi:10.1088/0143-0807/36/6/065010

The Drude formula of ac (frequency-dependent) electric conductivity has been established as a simple and practically useful model to understand the electromagnetic response of simple free-electron-like metals. In most textbooks of solid-state physics, the Drude formula is derived from either a classical equation of motion or the semiclassical Boltzmann transport equation. On the other hand, quantum-mechanical derivation of the Drude conductivity, which requires an appropriate treatment of phonon-assisted intraband transitions with small momentum transfer, has not been well documented except for the zero- or high-frequency case. Here, a lucid derivation of the Drude conductivity that covers the entire frequency range is presented by means of quantum kinetic equations in the density-matrix formalism. The derivation is straightforward so that advanced undergraduate students or early-year graduate students will be able to gain insight into the link between the microscopic Schrödinger equation and macroscopic transport.

Derivation of the Drude conductivity from quantum kinetic equations

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