Electronic structure of parallel two-dimensional electron systems in tilted magnetic fields

We report on a study of the electronic structure of two parallel two-dimensional 2D layer systems in tilted magnetic fields. Magnetic oscillations are studied by calculating the magnetization of the system as a function of field strength and tilt angle. The calculation is fully quantum mechanical and comparisons with semiclassical approximations are discussed. We find that a crossover occurs as a function of field strength between a region at weak perpendicular fields where semiclassical approximations are accurate and a region at stronger perpendicular fields where the probability of magnetic breakdown becomes large and semiclassical approximations fail. At strong perpendicular fields the parallel component of the magnetic field reduces the symmetric-antisymmetric gap, ${\mathrm{\Delta }}_{\mathrm{SAS}}$, associated with hopping between layers.