Conserved charges of order-parameter textures in Dirac systems

TL;DR

This paper derives a simple formula for the induced fermion current in two-dimensional Dirac systems with order-parameter textures, revealing conditions under which these textures carry conserved electrical charges, with applications to graphene and topological insulators.

Contribution

It provides a unified expression for induced fermion currents in Dirac systems with textures and identifies conditions for these textures to carry conserved electrical charges.

Findings

Every texture in three anticommuting order parameters induces a conserved charge.

Charge is the electrical charge if remaining order parameters are superconducting phase components.

Eight types of charged textures are possible in graphene and related 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.