Quantum transport of Dirac electrons in graphene in the presence of a spatially modulated magnetic field

TL;DR

This paper studies how a weak, periodic magnetic field affects electron transport in graphene, revealing oscillations in conductivity and comparing these effects with other systems, highlighting unique amplitude and phase characteristics.

Contribution

It provides analytical and numerical analysis of magnetoconductivity in magnetically modulated graphene, showing distinct oscillation behaviors compared to electrically modulated graphene and 2DEG systems.

Findings

Landau levels broaden into bands with oscillating width.

Weiss oscillations in conductivity are less damped by temperature in this system.

Oscillations are out of phase with electrically modulated graphene but in phase with 2DEG.

Abstract

We have investigated the electrical transport properties of Dirac electrons in a monolayer graphene sheet in the presence of a perpendicular magnetic field that is modulated weakly and periodically along one direction.We find that the Landau levels broaden into bands and their width oscillates as a function of the band index and the magnetic field.We determine the $\sigma_{yy}$ component of the magnetoconductivity tensor for this system which is shown to exhibit Weiss oscillations.We also determine analytically the asymptotic expressions for $\sigma_{yy}$.We compare these results with recently obtained results for electrically modulated graphene as well as those for magnetically modulated conventional two-dimensional electron gas (2DEG) system.We find that in the magnetically modulated graphene system cosidered in this work,Weiss oscillations in $\sigma_{yy}$ have a reduced amplitude compared to the 2DEG but are less damped by temperature while they have a higher amplitude than in the electrically modulated graphene system. We also find that these oscillations are out of phase by $\pi$ with those of the electrically modulated system while they are in phase with those in the 2DEG system.