  Motivated by electronic transport in graphene-like structures, we study the
diffusion of a classical point particle in Fermi potentials situated on a
triangular lattice. We call this system a soft Lorentz gas, as the hard disks
in the conventional periodic Lorentz gas are replaced by soft repulsive
scatterers. A thorough computational analysis yields both normal and anomalous
(super) diffusion with an extreme sensitivity on model parameters. This is due
to an intricate interplay between trapped and ballistic periodic orbits, whose
existence is characterized by tongue-like structures in parameter space. These
results hold even for small softness showing that diffusion in the paradigmatic
hard Lorentz gas is not robust for realistic potentials, where we find an
entirely different type of diffusion.
