Relativistic Crystalline Symmetry Breaking And Anyonic States In   Magnetoelectric Superconductors
  There exists a connection between the creation of toroidal moments (TM) and the breaking of the one-cell relativistic crystalline symmetry (RCS) associated to any given crystal into which non-trivial magnetoelectric coupling effects (ME) exist. Indeed, in this kind of crystals, any interaction between a charge carrier and an elementary magnetic cell can breaks the RCS of this previous given cell by varying, in the simplest case, the continuous defining parameters of the initial RCS. This breaking can be associated to a change of the initial Galilean proper frame of any given carrier to an "effective" one, into which the RCS of the interacting cell is kept. We can speak of a kind of "inverse" kineto-magnetoelectric effect. The magnetic groups compatible with such process have been computed. Moreover, one can notice that the TM's break the P and T symmetries but not the PT one as in anyons theories. This breaking creates so-called Nambu-Goldstone bosons generating "effective" magnetic monopoles. These consequences allow us to claim, first, that anyons are charge carriers associated with "effective" magnetic monopoles, both with TM's, and second, that ME can be highly considered in superconductors theory. 
Jacques L. Rubin