Problem: de Haas-van Alphen

        Magnetic field H is applied perpendicular to the layers of conduction in a quasi-two-dimensional material. The crystal structure of the layers is tetragonal with lattice spacing a=3.5 Å. The electron energy band within the layers is well described by the tight-binding approximation, and there is no energy dispersion in the third direction.

The resistance and other material properties exhibit oscillations as the field varies. The oscillation is periodic in 1/H and the period is G . What is the conduction electron density (in units of cm ) for this material? (Be careful: The effective mass approximation does not work in this problem!)