The problem of the electronic structure of a perfect tight-binding crystal under a constant magnetic field is studied. Quantitative analysis based on a method of continuous fractions is developed. This method is compatible with the magnetic translation group. Calculations are carried out for various fields and an interpolation scheme, valid for fields up to ${10}^6$ G, is presented. In the two directions perpendicular to the field, the density of electronic states consists of subbands—i.e., broadened levels—separated by gaps. The broadening is negligible for most levels. It is, however, paramount in narrow energy ranges close to two-dimensional saddle points, where for all practical purposes, the subbands merge into a single continuum. The resulting electronic structure is applied to study the magneto-optical response of a hypothetical simple-cubic crystal with an infinitely narrow core state. Wavelength and field modulations are discussed; excitonic effects are not included.

• Received 16 July 1975

DOI:https://doi.org/10.1103/PhysRevB.13.1595