  Confining Dirac fermions in graphene by electrostatic fields is a challenging
task. Electric quantum dots created by a scanning tunneling microscope (STM)
tip can trap zero-energy quasi-particles. The Lorentzian quantum well provides
a faithful, exactly solvable, approximation to such a potential, hosting
zero-energy bound states for certain values of the coupling constant. We show
that in this critical configuration, the system can be related to the free
particle model by means of a supersymmetric transformation. The revealed shape
invariance of the model greatly simplifies the calculation of the zero modes
and naturally explains the degeneracy of the zero energy.
