Isospin of topological defects in Dirac systems
Abstract
We study the Dirac quasiparticles in ddimensional 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 threedimensional Clifford algebras, are proven to be in general possible. We show how the particlehole 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.
 Publication:

Physical Review B
 Pub Date:
 February 2012
 DOI:
 10.1103/PhysRevB.85.085304
 arXiv:
 arXiv:1109.0577
 Bibcode:
 2012PhRvB..85h5304H
 Keywords:

 71.10.Pm;
 71.10.Li;
 72.80.Vp;
 74.20.Rp;
 Fermions in reduced dimensions;
 Excited states and pairing interactions in model systems;
 Pairing symmetries;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 7 PRB pages, one table, one figure