  The fermionic fields constructed from Elko have several unexpected
properties. They satisfy the Klein-Gordon but not the Dirac equation and are of
mass dimension one instead of three-half. Starting with the Klein-Gordon
Lagrangian, we initiate a careful study of the symmetries and interactions of
these fermions and their higher-spin generalisations. We find, although the
fermions are of mass dimension one, the four-point fermionic self-interaction
violates unitarity at high-energy. Therefore, it cannot be a fundamental
interaction of the theory. It follows that for the spin-half fermions, the
demand of renormalisability and unitarity forbids four-point interactions and
only allows for the Yukawa interaction. For fermions with spin j>1/2, they have
no renormalisable or unitary interactions. Since the theory is described by a
Klein-Gordon Lagrangian, the interaction generated by the local $U(1)$ gauge
symmetry which contains a four-point interaction, is excluded by the demand of
renormalisability. In the context of the Standard Model, these properties make
the spin-half fermions natural dark matter candidates.
