Effects of transverse electric fields on Landau subbands in bilayer zigzag graphene nanoribbons

The magneto-electronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space, are resulted from the competition between magnetic and quantum confinement effects. In bilayer system, the interlayer interactions lead to two groups of QLLs, one occurring at the Fermi level and the other one occurring at higher energies. Transverse electric fields are able to distort energy spectrum, tilt two groups of QLLs, and cause semiconductor-metal transition. From the perspective of wave functions, the distribution of electrons is explored, and the evolution of Landau states under the influence of electric fields is clearly discussed. More interestingly, the band mixing phenomena exhibited in the energy spectrum are related to the state mixing, which can be seen by the wave functions. The density of states, which could be verified through surface inspections and optical experiments, such as scanning tunneling spectroscopy and absorption spectroscopy, is provided at last.