Electron dynamics in graphene with spin-orbit couplings and periodic potentials

Area of Science:

• Condensed Matter Physics
• Materials Science

Background:

• Graphene exhibits unique electronic properties due to its Dirac cones.
• Spin-orbit couplings (SOC) significantly influence electron behavior in materials.
• Potential barriers modify electron transport and wave packet dynamics.

Purpose of the Study:

• To investigate the energy-momentum dispersion and wave packet dynamics of electrons in graphene.
• To analyze the effects of both Kane-Mele and Rashba spin-orbit couplings.
• To study the influence of single and periodic potential barriers on electron behavior.

Main Methods:

• Utilized continuum and lattice models for theoretical analysis.
• Examined energy-momentum dispersion relations.
• Simulated wave packet dynamics under various conditions.

Main Results:

• Identified coexistence of massless and massive Dirac states when Kane-Mele and Rashba SOC are equal.
• Demonstrated that SOC generally opens gaps at Dirac points, with exceptions for equal SOC.
• Observed perfect transmission of massless states and reflection of massive states at potential barriers.
• Found states localized along single potential barriers.
• Discovered six momentum-space points with minimal wave packet spreading in the absence of SOC.

Conclusions:

• The interplay between spin-orbit couplings and potential barriers leads to complex electronic behaviors in graphene.
• Specific conditions, like equal Kane-Mele and Rashba SOC, create unique gapless Dirac points.
• Electron states exhibit distinct responses to barriers, with implications for electronic device design.
• Understanding wave packet dynamics is crucial for controlling electron transport in graphene nanostructures.