  We theoretically study the non-Hermitian systems, the non-Hermiticity of
which arises from the unequal hopping amplitude (UHA) dimers. The
distinguishing features of these models are that they have full real spectra if
all of the eigenvectors are time-reversal (T) symmetric rather than
parity-time-reversal (PT) symmetric, and that their Hermitian counterparts are
shown to be an experimentally accessible system, which have the same
topological structures as that of the original ones but modulated hopping
amplitudes within the unbroken region. Under the reflectionless transmission
condition, the scattering behavior of momentum-independent reflectionless
transmission (RT) can be achieved in the concerned non-Hermitian system. This
peculiar feature indicates that, for a certain class of non-Hermitian systems
with a balanced combination of the RT dimers, the defects can appear fully
invisible to an outside observer.
