  We show that annihilating a pair of Dirac fermions implies a topological
transition from the critical semi-metallic phase to an Obstructed Atomic Limit
(OAL) insulator phase instead of a trivial insulator. This is shown to happen
because of branch-cuts in the phase of the wave functions, leading to non
trivial Zak phase along certain directions. To this end, we study their Z$_2$
invariant and also study the phase transition using Entanglement Entropy. We
use low energy Hamiltonians and numerical result from model systems to show
this effect. These transitions are observed in realistic materials including
strained graphene and buckled honeycomb group-V (Sb/As).
