  This paper focuses on additional inspections concerning the fermionic sector
of the Standard Model Extension (SME). In this context, our main effort in this
contribution is to investigate effects of Lorentz-symmetry violation (LSV) on
the Klein Paradox, the Zitterbewegung and its phenomenology in connection to
Condensed Matter Physics, Atomic Physics, and Astrophysics. Finally, we discuss
a particular realization of LSV in the Dirac equation, considering an asymmetry
between space and time due to a scale factor present in the linear momentum of
the fermion, but which does not touch its time derivative. We go further and
extend the implications of this asymmetry in the situation the scale factor
becomes space-time dependent to compute its influence on the kinematics of the
Compton effect with the extended dispersion relation for the fermion that
scatters the photon.
