Edge modes and non local conductance in graphene superlattices

Abstract

We study the existence of edge modes in gapped Moiré superlattices in graphene monolayer ribbons. We find that the superlattice bands acquire finite Chern numbers, which lead to a Valley Hall Effect. The presence of dispersive edge modes is confirmed by calculations of the band structure of realistic nanoribbons using tight binding methods. These edge states are only weakly sensitive to disorder, as short-range scattering processes lead to mean free paths of the order of microns. The results explain the existence of edge currents when the chemical potential lies within the bulk superlattice gap, and offer an explanation for existing non-local resistivity measurements in graphene ribbons on boron nitride.

References in corpus (15)

• The electronic properties of graphene
• Electronic States of Graphene Nanoribbons
• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• Detecting Topological Currents in Graphene Superlattices
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• Zero Energy Modes and Gate-Tunable Gap in Graphene on hexagonal Boron Nitride
• Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Localized states at zigzag edges of bilayer graphene
• Spontaneous Strains and Gap in Graphene on Boron Nitride
• Edge currents shunt the insulating bulk in gapped graphene
• Moiré band model and band gaps of graphene on hexagonal boron nitride
• Graphene on boron-nitride: Moiré pattern in the van der Waals energy
• Interactions and magnetism in graphene boundary states

Cited by in corpus (7)

• Flat bands, strains, and charge distribution in twisted-bilayer hBN
• Boundary Modes from Periodic Magnetic and Pseudomagnetic Fields in Graphene
• Valley current generation using biased bilayer graphene dots
• Emergent inhomogeneity and non-locality in a graphene field-effect transistor on a near-parallel moire superlattice of transition metal dichalcogenides
• Strain-Fluctuation-Induced Near-Quantization of Valley Hall Conductivity in Graphene Systems
• Spin-polarized superconducting phase in semiconducting system with next-nearest-neighbor hopping on the honeycomb lattice
• Connection between the semiconductor--superconductor transition and the spin-polarized superconducting phase in the honeycomb lattice