1109.0577 (Igor F. Herbut)

Isospin of topological defects in Dirac systems    [PDF]

Igor F. Herbut

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 non-trivial quantum numbers such as charge and spin. Here we
discuss their additional internal degree of freedom: irrespectively 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 such 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.

View original: http://arxiv.org/abs/1109.0577