Tuning electronic properties of bilayer Bernal graphene nanoribbon by magnetic modulation

This study shows that the electronic properties of bilayer Bernal graphene nanoribbon can be effectively tuned by a spatially modulated magnetic field. The electronic structures are significantly influenced by varying the field strength or the period of the modulated field. In addition, there exists competition between the magnetic confinement effect and the quantum confinement effect. The density of states (DOS) exhibits many asymmetric square-root divergent peaks due to the oscillatory parabolic subbands. These peaks can be classified into primary and secondary ones. The number, height, and energy of the peaks depend sensitively on the strength and the period of the modulated field. The evolution of the DOS peak energy with the field strength and the period is explored. The energies of primary peaks first exhibit linear, then square-root dependence on the field strength. On the other hand, the field strength dependence of the secondary peaks is purely square root. These theoretical predictions can be validated by STS or magneto-transmission measurements.