Circling Electrons in High Magnetic Fields

Abstract

In a magnetic field the motion of electric charges perpendicular to the field direction is deflected into circular orbits because of the Lorentz force. This deflection causes an increase in the electric resistance and the generation of the Hall voltage transverse to the current flow in the conductor. The orbital motion corresponds to a redistribution of the electrons in the conduction band onto Landau cylinders in momentum space. At high magnetic fields this leads to a periodic oscillation of the electronic crystal properties as a function of the magnetic field. Experimental studies of these oscillations yield information about the extreme cross-sections of the Fermi surface perpendicular to the magnetic field direction. The de Haas–van Alphen effect is discussed. In the restricted geometry of a two-dimensional electron gas, new quantum effects appear, such as the integer and the fractional quantum Hall effect.