In this study, we conducted a numerical investigation on the Hall conductance (σHall) of graphene based on the magnetic energy band structure calculated using a nonperturbative magnetic-field-containing relativistic tight-binding approximation (MFRTB) method. The nonperturbative MFRTB can revisit two types of plateaus for the dependence of σHall on Fermi energy. One set is characterized as wide plateaus (WPs). These WPs have filling factors (FFs) of 2, 6, 10, 14, etc. and are known as the half-integer quantum Hall effect. The width of WPs decreases with increasing FF, which exceeds the decrease expected from the linear dispersion relation of graphene. The other set is characterized by narrow plateaus (NPs), which have FFs of 0, 4, 8, 12, etc. The NPs correspond to the energy gaps caused by the spin-Zeeman effect and spin-orbit interaction. Furthermore, it was discovered that the degeneracy of the magnetic energy bands calculated using the nonperturbative MFRTB method leads to a quantized σHall.
@article{arxiv.2309.03444,
title = {Quantized Hall conductance in graphene by nonperturbative magnetic-field-containing relativistic tight-binding approximation method},
author = {Md. Abdur Rashid and Masahiko Higuchi and Katsuhiko Higuch},
journal= {arXiv preprint arXiv:2309.03444},
year = {2023}
}