Electrical manipulation of the edge states in graphene and the effect on the quantum Hall transport

Abstract

We investigate new properties of the Dirac electrons in the finite graphene sample under perpendicular magnetic field that emerge when an in-plane electric bias is also applied. The numerical analysis of the Hofstadter spectrum and of the edge-type wave functions evidentiate the presence of shortcut edge states that appear under the influence of the electric field. The states are characterized by a specific spatial distribution, which follows only partially the perimeter, and exhibit ridges that shortcut opposite sides of the graphene plaquette. Two kinds of such states have been found in different regions of the spectrum, their particular spatial localization being shown along with the diamagnetic moments that reveal their chirality. By simulating a four-lead Hall device, we investigate the transport properties and observe new, unconventional plateaus of the integer quantum Hall effect, which are associated with the presence of the shortcut edge states. The contributions of the novel states to the transmittance matrix that determine the new transport properties are shown. The shortcut edge states resulting from the splitting of the n=0 Landau level represent a special case, giving rise to non-trivial transverse and longitudinal resistance.

arXiv comment28 pages, 11 figures, accepted by Phys.Rev.B

References in corpus (19)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Quantum Spin Hall Effect in Graphene
• Electronic States of Graphene Nanoribbons
• Electronic Properties of Graphene in a Strong Magnetic Field
• Conductance quantization in mesoscopic graphene
• Novel electric field effects on Landau levels in Graphene
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Universal Scaling of Quantum Anomalous Hall Plateau Transition
• Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields
• Anomalous Edge Transport in the Quantum Anomalous Hall State
• Spectrum of $\pi$-electrons in Graphene As a Macromolecule
• Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene
• Unique nature of the lowest Landau level in finite graphene samples with zigzag edges: Dirac electrons with mixed bulk-edge character
• The orbital magnetization of single and double quantum dots in a tight binding model
• Theory of the quantum Hall effect in graphene
• Topological properties of the mesoscopic graphene plaquette: QSHE due to spin imbalance
• Specific Plateaus of the Quantum Hall Effect Induced by an Applied Bias

Cited by in corpus (6)

• Electronic and optical properties of graphene nanoribbons in external fields
• Magnetoelectronic and optical properties of nonuniform graphene nanoribbons
• Electrons trapped in graphene magnetic quantum dots with mass term
• Edge states mechanism for the anomalous quantum Hall effect in diatomic square lattice
• Zigzag edge states in graphene in the presence of in-plane electric field
• Peculiarities of the Landau level collapse in graphene ribbons in crossed magnetic and in-plane electric fields