  Geometric electron optics may be implemented in solid state when transport is
ballistic on the length scale of a device. Currently, this is realized mainly
in 2D materials characterized by circular Fermi surfaces. Here we demonstrate
that the nearly perfectly hexagonal Fermi surface of PdCoO2 gives rise to
highly directional ballistic transport. We probe this directional ballistic
regime in a single crystal of PdCoO2 by use of focused ion beam (FIB)
micro-machining, defining crystalline ballistic circuits with features as small
as 250nm. The peculiar hexagonal Fermi surface naturally leads to electron
self-focusing effects in a magnetic field, well below the geometric limit
associated with a circular Fermi surface. This super-geometric focusing can be
quantitatively predicted for arbitrary device geometry, based on the hexagonal
cyclotron orbits appearing in this material. These results suggest a novel
class of ballistic electronic devices exploiting the unique transport
characteristics of strongly faceted Fermi surfaces.
