  Weyl Semimetals (WSMs), a recently discovered topological state of matter,
exhibit an electronic structure governed by linear band dispersions and
degeneracy (Weyl) points leading to rich physical phenomena, which are yet to
be exploited in thin film devices. While WSMs were established in the
monopnictide compound family several years ago, the growth of thin films has
remained a challenge. Here, we report the growth of epitaxial thin films of NbP
and TaP by means of molecular beam epitaxy. Single crystalline films are grown
on MgO (001) substrates using thin Nb (Ta) buffer layers, and are found to be
tensile strained (1%) and with slightly P-rich stoichiometry with respect to
the bulk crystals. The resulting electronic structure exhibits topological
surface states characteristic of a P-terminated surface and linear dispersion
bands in agreement with the calculated band structure, and a Fermi-level shift
of -0.2 eV with respect to the Weyl points. Consequently, the electronic
transport is dominated by both holes and electrons with carrier mobilities
close to 10^3 cm2/Vs at room-temperature. The growth of epitaxial thin films
opens up the use of strain and controlled doping to access and tune the
electronic structure of Weyl Semimetals on demand, paving the way for the
rational design and fabrication of electronic devices ruled by topology.
