Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes

TL;DR

This paper explores how spatially varying potentials in graphene create new Dirac fermions and Landau levels, affecting magnetotransport and topological states, with potential applications in electronic switching and valleytronics.

Contribution

It provides a theoretical analysis of Landau levels, magnetotransport, and topological modes in superlattice-modified graphene, revealing novel effects and device implications.

Findings

Magnetic fields can reverse transport anisotropy in monolayer graphene.

Zero-energy Landau levels disperse due to superlattice potentials.

Kink bias in bilayer graphene induces topologically bound edge states.

Abstract

Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially periodic potential variations, lead to a modified bandstructure with extra finite-energy and zero-energy Dirac fermions with tunable anisotropic velocities. We theoretically show that transport in a weak perpendicular (orbital) magnetic field allows one to not only probe the number of emergent Dirac points but also yields further information about their dispersion. or monolayer graphene, we find that a moderate magnetic field can lead to a strong reversal of the transport anisotropy imposed by the SL potential, an effect which arises due to the SL induced dispersion of the zero energy Landau levels. This effect may find useful applications in switching or other devices. For bilayer graphene, we discuss the structure of Landau level wave functions and local density of states in the presence of a uniform bias, as well as in the presence of a kink in the bias which leads to topologically bound `edge states'. We consider implications of these results for scanning tunneling spectroscopy measurements, valley filtering, and impurity induced breakdown of the quantum Hall effect in bilayer graphene.