Quantized Hall conductance in graphene by nonperturbative magnetic-field-containing relativistic tight-binding approximation method

TL;DR

This paper numerically investigates graphene's quantum Hall conductance using a nonperturbative relativistic tight-binding method, revealing distinct plateau types linked to energy gaps and band degeneracies.

Contribution

It introduces a nonperturbative magnetic-field-containing relativistic tight-binding approach to analyze Hall conductance in graphene, uncovering new plateau behaviors and degeneracy effects.

Findings

Identification of wide and narrow Hall conductance plateaus

WPs have decreasing width with increasing filling factor

Degeneracy of magnetic bands leads to quantized Hall conductance

Abstract

In this study, we conducted a numerical investigation on the Hall conductance ($\sigma_{Hall}$) 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 $\sigma_{Hall}$ 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 $\sigma_{Hall}$.