  We propose the concept of birefringent Majorana fermions as collective
excitations of quantum interacting many-body states motivated by the already
known quasiparticles including Dirac fermions, birefringent Dirac fermions and
Majorana fermions. Low energy effective models are constructed to understand
the basic mathematical structures of equations of motion and physical
properties. We find that the equation of motion, with two different "speed of
light", describing birefringent Majorana fermions in condensed matter physics
is the birefringence version of the original Majorana equation of real
relativistic fermions.
