Graphene in external fields

TL;DR

This paper explores the behavior of graphene under external electromagnetic fields, deriving energy levels, Hall conductance sequences, and the Dirac equation in monochromatic waves, highlighting differences from conventional Dirac electrons.

Contribution

It provides a comprehensive formulation of graphene in external fields, predicts new Hall conductance sequences, and derives the second order Dirac equation in electromagnetic waves.

Findings

Restoration of Lorentz invariance in strong magnetic fields

Prediction of new Hall conductance sequence $rac{4q^2}{h}L$

Derivation of energy levels for orthogonal electric and magnetic fields

Abstract

A general discussion of graphene in external electromagnetic field is provided. In general, the formulation is not Lorentz invariant because of Zeeman energy. But it can be restored approxiamtely in the case of strong magnetic field, the condition when quantum Hall effect is observed. Besides obtaining the well-known Hall conductance $\frac{4q^2}{h}(L+1/2)$, we also predict that the sequence of Hall conductance $\frac{4q^2}{h}L$,which contains the newly observed Hall conductance $\frac{4q^2}{h}L$ for $L=0,1$, depending on the filling of Zeeman levels. The energy levels are obtained for general orthogonal constant electric and magnetic field. The second order Dirac equation is derived in applied monochromatic electromagnetic wave, and the major difference between graphene system and convetional Dirac electrons is pointed out.