Magnetoabsorption spectra of bilayer graphene ribbons with Bernal stacking

Abstract

Magnetoabsorption spectra of bilayer graphene ribbons with Bernal stacking are studied by the Peierls-coupling tight-binding method. When the magnetic confinement prevails over the quantum confinement, low-energy spectra chiefly exhibit many Landau peaks, which are strongly modified by the inter-ribbon interactions and the magnetic-field magnitude $(B)$. The spectra show denser Landau peaks in bilayer graphene ribbon than in a monolayer ribbon with the same ribbon width. The absorption frequencies of Landau peaks of a wide monolayer ribbon show the $\sqrt{B}$ dependence, while those of a bilayer ribbon exhibit a varying $B$-field dependence. In the spectra region $\ensuremath{\omega}\ensuremath{\le}100\text{ }\text{meV}$, the absorption frequencies of Landau peaks are linearly dependent on the magnetic-field magnitude. At $\ensuremath{\omega}\ensuremath{\ge}100\text{ }\text{meV}$, they evolve from the $B$ dependence to the $\sqrt{B}$ dependence with the increase in the field strength. The absorption frequencies of Landau peaks exhibit $\sqrt{B}$ dependence at $B\ensuremath{\ge}20\text{ }\text{T}$. The relationship between the magneto-optical properties and electronic structures (the state energies and wave functions) are explored. The Landau wave functions are illustrated and used to identify the optical selection rule.