  We investigate how photo-induced topological phase transitions and the
magnetic-field-induced quantum Hall effect simultaneously influence the Casimir
force between two parallel sheets of staggered two-dimensional (2D) materials
of the graphene family. We show that the interplay between these two effects
enables on-demand switching of the force between attractive and repulsive
regimes while keeping its quantized characteristics. We also show that doping
these 2D materials below their first Landau level allows one to probe the
photoinduced topology in the Casimir force without the difficulties imposed by
a circularly polarized laser. We demonstrate that the magnetic field has a huge
impact on the thermal Casimir effect for dissipationless materials, where the
quantized aspect of the energy levels leads to a strong repulsion that could be
measured even at room temperature.
