  Very recently the topological Weyl semimetal (WSM) state was predicted in the
noncentrosymmetric compounds TaAs, TaP, NbAs, and NbP and soon led to
photoemission and transport experiments to verify the presumed topological
properties such as Fermi arcs (unclosed Fermi surfaces) and the chiral anomaly.
In this work, we have performed fully \textit{ab initio} calculations of the
surface band structures of these four WSM materials and revealed the Fermi arcs
with spin-momentum-locked spin texture. On the (001) polar surface, the shape
of the Fermi surface depends sensitively on the surface terminations (cations
or anions), although they exhibit the same topology with arcs. The anion (P or
As) terminated surfaces are found to fit recent photoemission measurements
well. Such surface potential dependence indicates that the shape of the Fermi
surface can be manipulated by depositing guest species (such as K atoms), as we
demonstrate. On the polar surface of a WSM without inversion symmetry,
Rashba-type spin polarization naturally exists in the surface states and leads
to strong spin texture. By tracing the spin polarization of the Fermi surface,
we can also distinguish Fermi arcs from trivial Fermi circles. The four
compounds NbP, NbAs, TaP, and TaAs present an increasing amplitude of
spin-orbit coupling (SOC) in the band structure. By comparing their surface
states, we reveal the evolution of topological Fermi arcs from the
spin-degenerate Fermi circle to spin-split arcs when the SOC increases from
zero to a finite value. Our work will help us understand the complicated
surface states of WSMs and allow us to manipulate them, especially for future
spin-revolved photoemission and transport experiments.
