Zero modes and charged Skyrmions in graphene bilayer

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Bilayer graphene exhibits unique electronic properties due to its broken symmetry states and quadratic band crossing.
• Quantum anomalous Hall states and layer antiferromagnets are exotic phases of matter with potential technological applications.
• Skyrmions are topological spin textures that can host exotic electronic properties.

Purpose of the Study:

• To determine the electric charge of Skyrmions in specific electronic states within bilayer graphene.
• To investigate the role of vortex configurations and symmetry in these electronic states.
• To explore the implications for superconductivity arising from Skyrmion condensation.

Main Methods:

• Theoretical analysis of vortex configurations in bilayer graphene with broken symmetry states.
• Application of Kramers's theorem to understand the doubling of zero modes in vortex Hamiltonians.
• Investigation of the quantum anomalous spin Hall state and layer antiferromagnet properties.

Main Results:

• The electric charge of the Skyrmion is found to be four in the quantum anomalous spin Hall state.
• The electric charge of the Skyrmion is found to be zero in the layer antiferromagnet state.
• The number of zero modes in vortex configurations is doubled in bilayer graphene compared to single-layer graphene, explained by pseudo time-reversal symmetry.

Conclusions:

• Skyrmion condensation in the quantum anomalous spin Hall state of bilayer graphene is predicted to lead to a superconductor with an elementary charge of 4e.
• The study highlights the importance of topological defects and symmetry in understanding exotic electronic phases in 2D materials.
• The findings provide a theoretical basis for exploring novel superconducting states in graphene-based systems.