Interplay between hopping dimerization and quasi-periodicity on flux-driven circular current in an incommensurate Su–Schrieffer–Heeger ring

We report for the first time the phenomenon of flux-driven circular current in an isolated Su–Schrieffer–Heeger (SSH) quantum ring in presence of cosine modulation in the form of the Aubry–André–Harper (AAH) model. The quantum ring is described within a tight-binding framework, where the effect of magnetic flux is incorporated through Peierls substitution. Depending on the arrangements of AAH site potentials we have two different kinds of ring systems that are referred to as staggered and non-staggered AAH SSH rings. The interplay between the hopping dimerization and quasiperiodic modulation leads to several new features in the energy band spectrum and persistent current which we investigate critically. An atypical enhancement of current with increasing AAH modulation strength is obtained that gives a clear signature of transition from a low conducting phase to a high conducting one. The specific roles of AAH phase, magnetic flux, electron filling, intra- and inter-cell hopping integrals, and ring size are discussed thoroughly. We also study the effect of random disorder on persistent current with hopping dimerization to compare the results with the uncorrelated ones. Our analysis can be extended further in studying magnetic responses of similar kinds of other hybrid systems in presence of magnetic flux.