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Volkov-Pankratov surface bands arise in smooth topological interfaces, i.e.interfaces between a topological and a trivial insulator, in addition to thechiral surface state imposed by the bulk-surface correspondence of topologicalmaterials. These two-dimensional bands become Landau-quantized if a magneticfield is applied perpendicular to the interface. I show that the energy scales,which are typically in the 10-100 meV range, can be controlled both by theperpendicular magnetic field and the interface width. The latter can still bevaried with the help of a magnetic-field component in the interface. The Landaulevels of the different Volkov-Pankratov bands are optically coupled, and theirarrangement may allow one to obtain population inversion by resonant opticalpumping. This could serve as the elementary brick of a multi-level laser basedon Landau levels. Moreover, the photons are absorbed and emitted eitherparallel or perpendicular to the magnetic field, respectively in the Voigt andFaraday geometry, depending on the Volkov-Pankratov bands and Landau levelsinvolved in the optical transitions.

Topological interface states -- a possible path towards a Landau-level laser in the THz regime