  We investigated the pressure evolution of the electrical transport in the
almost compensated Weyl semimetal TaP. In addition, we obtained information on
the modifications of the Fermi-surface topology with pressure from the analysis
of pronounced Shubnikov-de Haas (SdH) quantum oscillations present in the
Hall-effect and magnetoresistance data. The simultaneous analysis of the Hall
and longitudinal conductivity data in a two-band model revealed an only weak
decrease in the electron- and hole charge-carrier densities up to 1.2 GPa,
while the mobilities are essentially pressure independent along the a-direction
of the tetragonal crystal structure. Only weak changes in the SdH frequencies
for B||a and B||c point at a robust Fermi-surface topology. In contrast to the
stability of the Fermi-surface topology and of the density of charge carriers,
our results evidence a strong pressure variation of the magnitude of transverse
magnetoresistance for B||a contrary to the results for B||c. We can relate the
former to an increase in the charge-carrier mobilities along the
crystallographic c-direction.
