We review recent progress toward a comprehensive understanding of electronic processes in HgTe-CdTe superlattices. The unique band structure is analyzed, and its incorporation into new theories for transport and magneto-optical properties is discussed. The calculations are compared with recent experimental results, including the observation of enhanced electron mobilities in modulation-doped and setback-modulation-doped structures. Many of the intentionally doped superlattices with strong three-dimensional dispersion display prominent quantum Hall features, in some cases at magnetic fields for which there is no energy gap between the minibands for successive Landau levels. The band structure theory has been extended to the case of HgTe-CdTe quantum wires. It is predicted that due to the small free carrier masses, lateral confinement effects are far larger than those observed in wide-gap systems. A number of new phenomena are expected in narrow-gap nanostructures.
