Electron Quantum Optics with Beam Splitters and Waveguides in Dirac Matter

An electron is a quantum particle and behaves as both a particle and a probability 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.