Diamagnetic Band-Structure Up To 2nd-Order In The Crystal Potential

The energy spectrum is calculated of a crystal electron in the presence of a magnetic field by using the Landau functions as basis with the periodic potential treated perturbatively. In contrast to the prevailing opinion which is based on first‐order effects only, our second‐order calculation predicts an observable broadening of the lower Landau levels. Furthermore, our quantum mechanical treatment gives a similar magnetic breakdown condition as the well‐known semiclassical considerations. Also the optical transition probability is determined approximately and from this an expression for the cyclotron mass is derived.