Momentum-independent reflectionless transmission in the non-Hermitian time-reversal symmetric system

• We investigate the non-Hermitian system with time reversal symmetry.
• The Hermitian counterpart is experimentally accessible system.
• The behavior of momentum-independent reflectionless transmission can be achieved.
• A balanced combination of reflectionless transmission dimers leads to invisibility.
• It paves an alternative way for the design of invisible cloaking devices.

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 (TT) symmetric rather than parity-time-reversal (PTPT) 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.