Possibility of massless Dirac fermions in an Aubry–André–Harper potential

In this study, we present a one-dimensional tight-binding model designed to explore the impact of electric fields on an incommensurate quantum system. We specifically focus on the Aubry–André–Harper model, a quasiperiodic model known to exhibit a metal–insulator transition at a critical potential value of λc = 2. This model combines Anderson and Aubry–André–Harper localization phenomena in a quantum system, leading to intriguing effects on the lattice band structure upon the application of an electric field F to the Aubry–André–Harper potential. Our investigation reveals that by choosing a specific value for the applied electric field, it becomes feasible to generate effective massless Dirac fermions within our Aubry–André–Harper system. Furthermore, we note that the extension or localization of the massless particle wave function is contingent upon the potential strength value λ within our incommensurate model. Importantly, our findings highlight the potential for detecting this intriguing phenomenon through experimental means.