  A notable feature of non-Hermitian systems with skin effects is the
sensitivity of their spectra and eigenstates to the boundary conditions. In the
literature, three types of boundary conditions-periodic boundary condition,open
boundary condition and a defect in the system as a boundary, are explored. In
this work we introduce the other type of boundary condition provided by a giant
atom. The giant atom couples to a nonreciprocal SuSchrieffer-Heeger chain at
two points and plays the role of defects. We study the spectrum and
localization of eigenstates of the system and find that the giant atom can
induce asymmetric zero modes. A remarkable feature is that bulk states might
localize at the left or the right chain-atom coupling sites in weak
localization regimes. This bipolar localization leads to Bloch-like states,
even though translational invariance is broken. Moreover, we find that the
localization is obviously weaker than the case with two small atoms or open
boundary conditions even in strong coupling regimes. These intriguing results
indicate that nonlocal coupling of giant atom to a nonreciprocal SSH chain
weakens localization of the eigenstates. We also show that the Lyapunov
exponent in the long-time dynamics in real space can act as a witness of the
localized bulk states.
