Mobility edges in non-Hermitian models with slowly varying quasiperiodic disorder

We investigate the appearance of mobility edges in a one-dimensional non-Hermitian tight-binding model with alternating hopping constants and slowly varying quasiperiodic on-site potentials. Due to the presence of a slowly varying exponent, the parity-time $(\mathcal{P}\mathcal{T})$ symmetry of this model is broken and its spectra are complex. It is found that the spectrum of this model can be divided into three different types of patterns depending on the magnitude of the quasiperiodic potential. As the amplitude of the potential increases from small to large, the initially well-defined mobility edges become blurred gradually and then eventually disappear for large-enough potential. This behavior of mobility edges is also confirmed by a detailed study of the winding number of complex spectra of this non-Hermitian model.