  We develop the theory of quantum friction in two-dimensional topological
materials. The quantum drag force on a metallic nanoparticle moving above such
systems is sensitive to the non-trivial topology of their electronic phases,
shows a novel distance scaling law, and can be manipulated through doping or
via the application of external fields. We use the developed framework to
investigate quantum friction due to the quantum Hall effect in magnetic field
biased graphene, and to topological phase transitions in the graphene family
materials. It is shown that topologically non-trivial states in two-dimensional
materials enable an increase of two orders of magnitude in the quantum drag
force with respect to conventional neutral graphene systems.
