Isospin of topological defects in Dirac systems

We study the Dirac quasiparticles in d-dimensional lattice systems of electrons in the presence of domain walls (d = 1), vortices (d = 2), or hedgehogs (d = 3) of superconducting and/ or insulating, order parameters, which appear as mass terms in the Dirac equation. Such topological defects have been known to carry nontrivial quantum numbers, such as charge and spin. Here we discuss their additional internal degree of freedom: irrespective of the dimensionality of space and the nature of orders that support the defect, an extra mass order parameter is found to emerge in their core. Six linearly independent local orders, which close two mutually commuting three-dimensional Clifford algebras, are proven to be in general possible. We show how the particle-hole symmetry restricts the defects to always carry the quantum numbers of a single effective isospin 1/2, quite independently of the values of their electric charge or true spin. Examples of this new degree of freedom in graphene and on surfaces of topological insulators are discussed.