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Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

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Emerging zero modes for graphene in a periodic potential.

L Brey¹, H A Fertig

¹Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco 28049, Spain.

Physical Review Letters

|August 8, 2009

Summary

A periodic potential induces new zero-energy electronic states in graphene, linked to wave function phases and overdamped particle motion. These novel states, confirmed numerically, manifest as conductance resonances, creating induced Dirac points.

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Mechanics

Background:

Graphene exhibits unique electronic properties governed by its Dirac cone band structure.
Periodic potentials can significantly alter electronic states in materials.
Understanding these effects is crucial for developing novel electronic devices.

Purpose of the Study:

To investigate the impact of a periodic potential on graphene's electronic states and conductance.
To identify the conditions for the emergence of new zero-energy states.
To explore the relationship between these states and conductance resonances.

Main Methods:

Theoretical analysis of electronic states under a cosine potential V(x) = V₀cos(G₀x).
Investigation of wave function phases and their relation to periodic solutions of an overdamped particle equation.
Numerical solutions of the Dirac equation to confirm state existence and chirality.
Analysis of conductance resonances associated with induced Dirac points.

Main Results:

New zero-energy states emerge when J₀(2V₀/ħv<0xE1><0xB5><0xA3>G₀) = 0.
The phase of these states relates to periodic solutions of an overdamped particle's equation of motion.
Numerical simulations confirm the existence and chirality of these induced Dirac points.
Conductance resonances are observed coinciding with the emergence of these states.

Conclusions:

Periodic potentials can induce novel zero-energy states in graphene.
These states are characterized by specific wave function properties and chirality.
The phenomenon is accompanied by observable conductance resonances, indicating potential for tunable electronic properties.