Theory of Shubnikov-de Haas oscillations
Peerzada, Lubna Naseem
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The first three chapters are preliminaries. Basic concepts in solid-state theory, electric conduction and the Hall effect and the magnetic susceptibility are discussed. The de Haas-van Alphen (dHvA) oscillations in the susceptibility and the Shubnikov-de Haas (ShdH) oscillations arise from the quasi-periodic variation of the density of states with the magnetic field. The dHvA oscillations are dealt in Chapter 4. A quantum theory is developed for the Shubnikov-de Haas oscillation in GaAs/AlGaAs. The envelope of the oscillation for the magnetoresistance is shown to be proportional to [sinh(2π 2 k B TM * / hω c )] -1 , where M * is the carrier mass. Comparison between theory and experiment directly gives the M *-value: M * [approximate] 0.30 m e which is much greater than the cyclotron effective mass m * [approximate] 0.067 m e . The carriers are likely to be the c-fermions, each electron with two flux quanta. The theory avoids the use of the Dingle temperature mysteriously arising Landau level damping. The susceptibility is an equilibrium property which must be calculated without introducing the scattering mechanism.