  The Casimir effect arises from the zero-point energy of particles in momentum
space deformed by the existence of two parallel plates. For degrees of freedom
on the lattice, its energy-momentum dispersion is determined so as to keep a
periodicity within the Brillouin zone, so that its Casimir effect is modified.
We study the properties of Casimir effect for lattice fermions, such as the
naive fermion, Wilson fermion, and overlap fermion based on the M\"obius
domain-wall fermion formulation, in the $1+1$, $2+1$, and $3+1$ dimensional
spacetime with the periodic or antiperiodic boundary condition. An oscillatory
behavior of Casimir energy between odd and even lattice size is induced by the
contribution of ultraviolet-momentum (doubler) modes, which realizes in the
naive fermion, Wilson fermion in a negative mass, and overlap fermions with a
large domain-wall height. Our findings can be experimentally observed in
condensed matter systems such as topological insulators and also numerically
measured in lattice simulations.
