Abstract
The motion of Bloch electrons in homogeneous magnetic fields is reduced without approximations to, at most, two dimensions in the general three-dimensional case, i.e., for arbitrary crystal potential, arbitrary field-lattice geometry, and all rational fields. This is done by fully exploiting a canonical transformation and by constructing with the aid of ray-group projection operators generalized functions, which separate off one degree of freedom. Previous ad hoc reductions to one dimension for essentially two-dimensional situations are recovered and explained. The solutions of the resulting lower-dimensional effective Schrödinger equations are functions of generalized coordinates. They are converted into the real-space wave functions by means of a contact transformation; their local and global properties are investigated. The results presented allow first-principles calculations of diamagnetic band structures and wave functions to realistic systems.
- Received 8 September 1981
DOI:https://doi.org/10.1103/PhysRevB.25.2358
©1982 American Physical Society