Electric-field-induced destruction of quasi-Landau levels in bilayer graphene nanoribbons

The magneto-electronic properties of bilayer zigzag graphene nanoribbons are investigated by the Peierls tight-binding method. In the presence of magnetic fields, Landau quantization leads to the formation of Landau subbands. For the bilayer nanoribbons, these subbands are partially dispersionless in k-space and are called quasi-Landau levels (QLLs). Perpendicular electric fields, serving as the top gate, push the QLLs to higher state energy and split the flat subbands. From the evidence of band structure and density of states, the QLLs remain dispersionless and the corresponding peaks are still the main structure of density of states, which means that the material properties related to the QLLs are unchanged. However, the wave functions present a totally different evidence that the Landau wave functions are severely mixed, and the corresponding material properties would be strongly affected or destroyed. The wave functions provide an effective way to comprehend the characteristics of the flat subbands and Landau subbands. The energy spectra, density of states, and wave functions are discussed in detail.