Conserved charges of order-parameter textures in Dirac systems

Abstract

A simple expression for the induced fermion current in the presence of a texture in mass-order-parameters in two-dimensional condensed-matter Dirac systems is derived using the representation theory of Clifford algebras. In particular, it is shown that every texture in three mutually anticommuting order parameters, in graphene for example, implies an induced density of a properly defined conserved charge. The sufficient condition for the general charge to be the familiar electrical charge is that the remaining two anticommuting order parameters allowed by the particle-hole symmetry are the two phase components of some superconducting order. This allows eight different types of electrically charged textures in graphene or in the $\pi$-flux Hamiltonian on the square lattice. Generalized charge of mass-textures on the surfaces of thin films of topological insulators, or in spinless Dirac fermions hopping on the honeycomb lattice is also discussed.

6 revtex pages; updated references, cosmetic changes; published version

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Cited by in corpus (9)

• Wess-Zumino-Witten Terms in Graphene Landau Levels
• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
• 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
• 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
• Topological quantum control: Edge currents via Floquet depinning of skyrmions in the $\nu =0$ graphene quantum Hall antiferromagnet