Quantum Magnetotransport

Abstract

A magnetic field causes electrons to rotate in the plane perpendicular to this field. As a result (see Sec. 11), the anisotropy of the response along the field and in the plane perpendicular to the field appears, and the kinetic coefficients are modified considerably if the cyclotron frequency exceeds the relaxation rate. Further qualitative modifications take place under the transition from the quasi-classical fields satisfying Eq. (9.35) to quantizing magnetic fields. Even when the cyclotron energy is still small in comparison to the Fermi energy, there appear oscillations of the conductivity as a function of the magnetic field. Another kind of oscillations takes place because of interaction of electrons with the dispersionless optical phonons. In the region where the cyclotron energy is comparable to the Fermi energy, the validity condition (7.21) of the kinetic equation (7.13) must be critically reconsidered because of accumulation of electrons at the bottoms of the Landau levels, where the density of states (5.16) increases according to the inverse square root dependence, leading to an increase in the relaxation rate. In the case of 2D electron gas in the magnetic field perpendicular to the 2D plane, the density of states of free electrons is represented by a set of δ-peaks associated with the Landau levels; see Sec. 16. For this reason, any description of electron transport based upon the quasi-classical kinetic equation (9.34) becomes invalid, and completely new kinetic phenomena, such as the quantum Hall effect, appear. The quantization of electron states in magnetic fields also has a considerable influence on the optical properties of dielectrics. There exists an anisotropy of the response due to virtual interband transitions, and the characteristics of exciton absorption are dramatically modified.