Localized states in graphene nanoribbons.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Graphene nanoribbons exhibit unique electronic properties near the Fermi level.
• Understanding wave packet dynamics is crucial for nanoscale transport phenomena.

Purpose of the Study:

• To investigate spatially localized states in graphene nanoribbons.
• To explore the influence of edge geometry, nonlinearity, and disorder on these states.

Main Methods:

• Utilizing the tight-binding model with nearest neighbor interactions.
• Monitoring time evolution of wave packets.
• Applying the discrete nonlinear Schrödinger equation model.
• Introducing random on-site energies to simulate disorder.

Main Results:

• Armchair nanoribbons exhibit flat band states localized across the width.
• Zigzag nanoribbons show partially flat band states localized transversely and longitudinally.
• Nonlinearity and disorder lead to wave packet spreading and exponential localization, respectively.
• Identified distinct localization mechanisms including edge geometry, nonlinearity, and disorder.

Conclusions:

• Spatially localized states in graphene nanoribbons arise from diverse origins.
• These localization phenomena are critical for wave propagation and transport in 2D nanostructures.
• Findings have implications for honeycomb lattice systems in photonics, cold atoms, and beyond.