Generic mobility edges in a class of non-Hermitian quasicrystals

We present approximate solutions for the mobility edge (ME) in a specific class of one-dimensional non-Hermitian (NH) quasicrystals delineating between localized and extended states. These NH quasicrystals exhibit a combination of nonreciprocal hopping terms and imaginary phase factors. Our analytical approach is supported by rigorous numerical calculations, demonstrating significant accuracy. Furthermore, our ansatz aligns closely with the established limiting cases of the NH Aubry–André–Harper (AAH) and Ganeshan–Pixley–Das Sarma (GPD) models, which possess exact results, thereby enhancing the credibility of our approach. Additionally, we have examined their dynamic properties and identified distinct behaviors in different regimes. Our research offers a practical methodology for estimating the position of MEs in a category of NH quasicrystals that break duality.