  The magnetoelectronic 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 apparently seen in 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.
