THE MASS OF THE ELECTRON IN GaAs/AlGaAs BY SHUBNIKOV-DE HAAS EFFECT AND THE SPIN-CHARGE LOCKING

The energy of the free electron gas is calculated in three dimensions. In this calculation an integral over the wave vector space occurs which was solved by Dingle. In the low temperature approximation the integral over the Fermi distribution leads to x/sinh x type expression, called the Dingle’s formula. The spin symmetry is found to modify this formula which determines the oscillation amplitude of resistivity as a function of magnetic field, called the Shubnikov-de Haas effect. The theory introduces the effective charge so that the cyclotron frequency gets fractionalized resulting into m/ν± which for ν±=1 becomes m, the electron mass. Thus we have taken into account, the spin-charge fractions, to obtain the correct mass. For example, at certain magnetic field 1.5m is found instead of m. The Shubnikov-de Haas effect uses quantization of Landau levels but not the flux quantization. Hence we find that there is a “quantized Shubnikovde Haas effect” which measures m/h . We determine that when fractional values of ν± are taken into account, the mass of the electron, equal to the band mass in GaAs/AlGaAs is obtained.