The Shubnikov-De Haas effect and the magnetic freeze out

Abstract

The oscillations in the magnetoresistance have been observed for the first time by Shubnikov and de Haas on Bismuth (1). The observed oscillations were an evidence of the quantum effect induced by the magnetic field on the energy states. Few studies have been reported on semiconductors until 1961 (2), when generation of strong magnetic fields became possible. We consider first the case of standard semiconductors with isotropic and parabolic bands. The conditions for oscillations can be found starting from the eigenvalues of electron in a magnetic field B along the Z axis : ~2 k~ E = (n +½) ~c + + ½g # B 2m • -where mc,= eB/m ~ is the cyclotron