  A diffraction problem for a flat Chern-Simons layer at plane boundary of a
dielectric half space is solved. The Casimir energy of two dielectric half
spaces with Chern-Simons layers at plane-parallel boundaries separated by a
vacuum slit is derived. Crossing from the repulsive to the attractive Casimir
force is analyzed for two Au and two Si half spaces with boundary Chern-Simons
layers. Boundary quantum Hall layers in external magnetic field lead to Casimir
repulsion at nanoscales. We discuss features that make systems with boundary
quantum Hall layers unique for force measurements and search of long-range
interactions beyond electromagnetism.
