Zero modes and charged Skyrmions in graphene bilayer

Abstract

We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer-antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers' theorem implied by the "pseudo time reversal" symmetry of the vortex Hamiltonian. Disordering the quantum anomalous spin Hall state by Skyrmion condensation should produce a superconductor of an elementary charge 4e.

4+ pages, one table, one figure; (v2) improved pedagogy, new expression for the Pontryagin index derived, additional explanations; (v3) new and updated references, minor typos corrected, published version

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Cited by in corpus (19)

• The space group classification of topological band insulators
• Magnetic catalysis and axionic charge-density-wave in Weyl semimetals
• Colloquium: Quantum skyrmionics
• Classification of massive and gapless phases in bilayer graphene
• Magnetic Skyrmions coupled to fermions
• Charge-$2e$ Skyrmion condensate in a hidden order state
• Deconfined criticality in bilayer graphene
• Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
• Conserved charges of order-parameter textures in Dirac systems
• Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice
• Zero modes of the generalized fermion-vortex system in magnetic field
• Gapless vortex bound states in superconducting topological semimetals
• Skyrmions in a density wave state: a mechanism for chiral superconductivity
• Competing Orders and Anomalies
• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order
• Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene
• Half vortex and fractional electrical charge in two dimensions
• Zero modes and index theorems for non-Hermitian Dirac fermions