  We report on a simple scheme that may present a non-trivial geometric Zak
phase ($\Phi_{Zak}$) structure, which is based on a discrete-time quantum walk
architecture. By detecting the Zak phase difference between two trajectories
connecting adjacent Dirac points where the quasi-energy gap closes for opposite
values of quasi-momentum ($k$), it is possible to identify geometric
invariants. These geometric invariants correspond to
$|\Phi_{Zak}^{+(-)}-\Phi_{Zak}^{-(+)}|=\pi$ and
$|\Phi_{Zak}^{+(-)}-\Phi_{Zak}^{+(-)}|=0$, we argue that this effect can be
directly measured.
