PT–symmetric tight-binding model with asymmetric couplings

We study spectral and transport properties of one-dimensional (1D) tight-binding PT–symmetric chains with non-equal consecutive couplings, i.e. asymmetric couplings. Based on the transfer matrix method, we obtain analytical expressions for the transmission and reflection coefficients for any values of the model parameters. These expressions, given in a very compact form, separately imbed the generic energy dependence, valid for any periodic structure, as well as specific properties of the dimers composing the 1D scattering chains. Our main interest is in the specific properties of the left/right reflections which are due to the PT–symmetric structure of the model. We have found that for the asymmetric coupling, there is no one-to-one correspondence between the degeneracy of the transfer matrix eigenvalues and PT–symmetric transport properties, such as the unidirectional reflectivity. We show that this correspondence, however, holds in the S−matrix approach, both for symmetric and asymmetric couplings. •We study spectral and transport properties of 1D tight-binding PT–symmetric chains with asymmetric couplings.•We obtain analytical expressions for the transmission and reflection coefficients for any values of the model parameters.•We found a new type of specific points in the spectrum responsible for unidirectional reflectivity.