Fractional Statistics of Topological Defects in Graphene and Related Structures

We show that fractional charges bound to topological defects in the recently proposed time-reversal-invariant models on honeycomb and square lattices obey fractional statistics. The effective low-energy description is given in terms of a “doubled” level-2 Chern-Simons field theory, which is parity and time-reversal invariant and implies two species of semions (particles with statistical angle $\pm \pi /2$) labeled by a new emergent quantum number that we identify as the fermion axial charge.

Figure 1

(a) Adiabatic formation of a vortex from a uniform, vortex-free configuration. The arrows represent the direction of $\widehat{\mathit{\phi }}$ along the $y=0$ cut through the vortex center. (b) Feynman diagram used to calculate the fermion current. Solid lines represent the fermion propagator $G(p)=(\mathrm{p̸}-m{)}^{-1}$.