  We construct a Darboux transformation for a class of two-dimensional Dirac
systems at zero energy. Our starting equation features a position-dependent
mass, a matrix potential, and an additional degree of freedom that can be
interpreted either as a magnetic field perpendicular to the plane or a
generalized Dirac oscillator interaction. We obtain a number of
Darbouxtransformed Dirac equations for which the zero energy solutions are
exactly known.
