The mass of the electron in Shubnikov-de Haas effect:Spin-charge locking

At low temperatures, the integration over the Fermi distribution leads to x/$\sin$h x type expression which is 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. The theory introduces the effective charge so that the cyclotron frequency gets fractionalized resulting into m/$\nu_{\pm}$. At a 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 S-dH effect'' which measures the m/h$^2$. We determine that when fractional values of the filling factor are taken into account, the mass of the electron, equal to the band mass is obtained. \newline 1. K. N. Shrivastava, Phys. Lett. A113, 435(1986). \newline 2. K. N. Shrivastava, Phys. Lett. A 326,469(2004). \newline 3. K. N. Shrivastava, Introduction to quantum Hall effect, Nova Sci. Pub. N.Y. (2002).