Quantum transport theory of electrons in solids: A single-particle approach

Rammer J.

The electronic transport theory of semiconductors is not, from a first-principles point of view, as well understood as is that of metals, where the degeneracy of the Fermi system leads to a simplified but comprehensive theory. In the case of semiconductors, degeneracy usually plays no simplifying role at all. However, in many transport problems of current interest one is effectively dealing with the equivalent of a single particle interacting with an environment, e.g., a heat bath or a random potential. In view of this, the author presents a simple formalism for the quantum dynamics of a single continuous degree of freedom. The quantum-statistical description is in terms of the density matrix, and the Feynman rules for a standard treatment of the density matrix are presented and illustrated by applications to problems of current interest. It is shown that such an effect as, for example, the intracollisional field effect, which in the past has been dealt with using complicated formalisms, in the present treatment is described in an elementary way. The single-particle approach conveniently displays the interference aspect of quantum-mechanical transport, as is discussed in a treatment of the weak localization effect in disordered conductors. The real-space representation of quantum transport is stressed, as is appropriate for a proper discussion of mesoscopic physics. The author treats the connection between the linear-response formalism and the Landauer approach by expressing the conductance in terms of the scattering properties of a sample. He also discusses the conductance fluctuations of mesoscopic samples.