Bloch Electrons in Crossed Electric and Magnetic Fields

Abstract

The purpose of this chapter is to describe recent theoretical and experimental studies on the properties of electrons in solids in the presence of crossed electric and magnetic fields. Semiconducting materials are best suited for such studies for the following reasons. First, the relatively high resistivity of semiconductors makes it possible to apply electric fields of the order of 10³ V/cm in pure materials and 10⁴-10⁵ V/cm in reverse-biased p-n junctions. Second, the small effective masses of electrons makes it possible for one to observe the magnetic field effects clearly, since the separation between Landau levels is given in terms of ℏω _c = ℏeH/mc. For a magnetic field of H = 100 kG and the free-electron mass this is equal to ~0.001 eV, so that in semiconductors like InSb (m ≈ 0.013 m ₀) energy separations of the order of 0.1 eV are achievable. Finally, due to low free-carrier densities a thin slab of a semiconducting material can transmit a light beam fairly well, which greatly facilitates the optical studies. Also, as we shall see later, narrow forbidden energy gaps, with resulting strong interaction between the conduction and valence bands, introduce a variety of interesting physical effects.

Supported by the U. S. Air Force Office of Scientific Research.