Role of electrical field in quantum Hall effect of graphene

TL;DR

This paper investigates how an electrical field influences the quantum Hall effect in graphene, revealing that the field can alter Landau levels and affect the quantization of Hall conductance, especially near critical field strengths.

Contribution

It provides a theoretical analysis of the impact of electrical fields on Landau levels and Hall conductance in graphene, highlighting the conditions leading to conductance saturation.

Findings

Electrical field causes Landau level broadening and overlap.

Quantized Hall conductance remains independent of the field under certain conditions.

Near critical electrical fields, Hall conductance saturation is observed.

Abstract

The ballistic motion of carriers of graphene in an orthogonal electromagnetic field is investigated to explain Hall conductance of graphene under experimental conditions. With the electrical field, all electronic eigen-states have the same expectation value of the velocity operator, or classically, all carriers move in cycloids with the same average velocity. The magnitude of this velocity is just appropriate to generate the quantized Hall conductance which is in turn exactly independent of the external field. Electrical field changes each Landau level into a bundle of energies, whose overlap in large fields destroys the quantized Hall conductance. As the electrical field tends to the critical point, Landau level expansion occurs. As a result, saturation of the Hall conductance may be observed.