  An electron behaves as both a particle and a wave. On account of this it can
be controlled in a similar way to a photon and electronic devices can be
designed in analogy to those based on light when there is minimal excitation of
the underlying Fermi sea. Here splitting of the electron wavefunction is
explored for systems supporting Dirac type physics, with a focus on graphene
but being equally applicable to electronic states in topological insulators,
liquid helium, and other systems described relativistically. Electron
beam-splitters and superfocusers are analysed along with propagation through
nanoribbons, demonstrating that the waveform, system geometry, and energies all
need to balance to maximise the probability density and hence lifetime of the
flying electron. These findings form the basis for novel quantum electron
optics.
