Peculiar Nature of Snake States in Graphene

TL;DR

This paper investigates the unique properties of snake states in graphene under non-uniform magnetic fields, revealing their peculiar current distribution and the coexistence of surface states, which differ from traditional 2DEG systems.

Contribution

It demonstrates the peculiar nature of snake states in graphene, including their local current imbalance and the existence of surface states, highlighting differences from conventional 2DEG snake states.

Findings

Snake states in graphene exhibit locally uncompensated current.

Surface states coexist with snake states in finite samples.

Distinct properties arise from Dirac fermion dynamics in graphene.

Abstract

We study the dynamics of the electrons in a non-uniform magnetic field applied perpendicular to a graphene sheet in the low energy limit when the excitation states can be described by a Dirac type Hamiltonian. We show that as compared to the two-dimensional electron gas (2DEG) snake states in graphene exibit peculiar properties related to the underlying dynamics of the Dirac fermions. The current carried by snake states is locally uncompensated even if the Fermi energy lies between the first non-zero energy Landau levels of the conduction and valence bands. The nature of these states is studied by calculating the current density distribution. It is shown that besides the snake states in finite samples surface states also exist.