  We study the Casimir effect in a system composed of two Weyl semimetals
(WSMs) separated by a gap filled with a chiral medium. We calculate the optical
response of the material to chiral photons in order to calculate the Casimir
force. We find that if the medium between the two WSMs is a Faraday material, a
repulsive Casimir force can be obtained, and for realistic experimental
parameters its magnitude can be greatly enhanced at short distances of a few
microns Moreover, in the system under consideration various parameters can be
modified. Some of them are intrinsic to the materials employed (the absolute
value of the Hall conductivity of the WSM, the Verdet constant of the Faraday
material), while some of them can be manipulated externally even for a fixed
sample, such as the external magnetic field and the orientation of the plates
which determines the sign of their conductivity. Suitable combinations of these
parameters can be used to switch from attraction to repulsion, and to place the
trapping distance, in which no force acts on the plates, at any desired
distance between them.
