  The quantum field operator for spin-half Elko describes a massive
self-interacting fermionic dark matter candidate of mass dimension one. It has
been shown that the theory has a built-in violation of the Lorentz symmetry and
a well-defined element of non-locality in the form of a preferred direction.
This note shows that quantum field operators constructed using spin-half and
higher-spin Elko violate Lorentz symmetry from first principle. Subsequently,
we study the kinematics of Elko and its quantum field operator for any spin
along the preferred direction.
