Critical wavefunctions in disordered graphene.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Physics

Background:

• Understanding electronic states in doped graphene is crucial for its electronic applications.
• Non-localized states can significantly alter material properties, bridging metallic and insulating behaviors.
• Previous studies have explored various aspects of graphene's electronic structure under doping.

Purpose of the Study:

• To investigate the presence and nature of non-localized states in doped graphene.
• To characterize the behavior of wavefunctions in the presence of random impurities.
• To determine if graphene exhibits intermediate states between metallic and insulating regimes.

Main Methods:

• Performed a scaling analysis of wavefunction moments, specifically inverse participation ratios (IPRs).
• Utilized a tight-binding Hamiltonian model incorporating nearest and next-nearest neighbor interactions.
• Introduced random substitutional impurities to simulate doping effects.

Main Results:

• Identified non-normalizable wavefunctions exhibiting a critical power-law decay.
• Observed electronic behavior intermediate between that of metals and insulators.
• Demonstrated the robustness of the power-law exponent distribution against system size and inclusion of next-nearest neighbors.

Conclusions:

• Doped graphene exhibits non-localized states characterized by critical power-law decay.
• These states represent a unique electronic regime distinct from typical metals and insulators.
• The findings are consistent across different model parameters, highlighting the fundamental nature of these states in doped graphene.