The response of thin films of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ to a strong perpendicular magnetic field is investigated by performing magnetic band-structure calculations for a realistic multiband tight-binding model. Several crucial features of Landau quantization in a realistic three-dimensional topological insulator are revealed. The $n=0$ Landau level is absent in ultrathin films, in agreement with experiment. In films with a crossover thickness of five quintuple layers, there is a signature of the $n=0$ level, whose overall trend as a function of magnetic field matches the established low-energy effective-model result. Importantly, we find a field-dependent splitting and a strong spin polarization of the $n=0$ level, which can be measured experimentally at reasonable field strengths. Our calculations reveal mixing between the surface and bulk Landau levels, which causes the character of the levels to evolve with magnetic field.

• Received 4 November 2014
• Revised 10 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.075430