  The electronic structures and topological properties of transition metal
dipnictides $XPn_2$ ($X$=Ta, Nb; $Pn$=P, As, Sb) have been systematically
studied using first-principles calculations. In addition to small bulk Fermi
surfaces, the band anticrossing features near the Fermi level can be identified
from band structures without spin-orbit coupling, leading to nodal lines in all
these compounds. Inclusion of spin-orbit coupling gaps out these nodal lines
leaving only a pair of disentangled electron/hole bands crossing the Fermi
level. Therefore, the low energy physics can be in general captured by the
corresponding two band model with several isolated small Fermi pockets.
Detailed analysis of the Fermi surfaces suggests that the arsenides and
NbSb$_2$ are nearly compensated semimetals while the phosphorides and TaSb$_2$
are not. Based on the calculated band parities, the electron and hole bands are
found to be weakly topological non-trivial giving rise to surface states. As an
example, we presented the surface-direction-dependent band structure of the
surfaces states in TaSb$_2$.
