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.
Categories: quant-ph cond-mat.mes-hall