  By using two-component approach to the one-dimensional effective mass Dirac
equation bound states are investigated under the effect of two new
non-PT-symmetric, and non-Hermitian, exponential type potentials. It is
observed that the Dirac equation can be mapped into a Schr\"{o}dinger-like
equation by rescaling one of the two Dirac wave functions in the case of the
position dependent mass. The energy levels, and the corresponding Dirac
eigenfunctions are found analytically.
