Theory of the integer quantum Hall effect in graphene

Difference Between Far-Infrared Photoconductivity Spectroscopy and Absorption Spectroscopy: Theoretical Evidence of the Electron Reservoir Mechanism

“…Their values may depend on i, but the chemical potential should take the same value. This is the mechanism of the electron reservoir model proposed by Toyoda and Zhang [6] to explain the integer quantum Hall effect observed in graphene. The SCLRA can be applied to each subsystem to calculate the magnetoplasmon dispersion.…”

“…It is, therefore, of paramount significance to verify the correctness of the proposed mechanism by carefully examining as many different experiments as possible. In this Letter we investigate the measurement of magnetoplasmon frequency by two different experimental methods carried out by Holland et al [1] and show that their findings provide clear theoretical evidence for the mechanism of the ER proposed in [6]. We also propose a new experiment that would validate the proposed mechanism of the electron reservoir model.…”

“…Among many theoretical models of the integer quantum Hall effect [2], the ERM [3][4][5][6][7] can reproduce the quantum Hall resistivity as a function of the gate voltage, magnetic induction, and temperature in perfect agreement with experiment. Nevertheless, the original idea [3] that the electron reservoir (ER) is due to donor impurity levels had been believed unlikely [8].…”

“…It was found that the mechanism can be explained by considering nonuniform electron density distribution in the two-dimensional electron system (2DES) caused by the Lorentz force. This can happen only when there are both a dc current and a perpendicular magnetic field in the 2DES [6]. The proposed mechanism should provide an important missing piece in the ERM for the integer quantum Hall effect.…”

“…Nevertheless, the original idea [3] that the electron reservoir (ER) is due to donor impurity levels had been believed unlikely [8]. The unknown mechanism of the ER had been obscuring the validity of the ERM for decades until it was finally revealed very recently [6]. It was found that the mechanism can be explained by considering nonuniform electron density distribution in the two-dimensional electron system (2DES) caused by the Lorentz force.…”