Fractional statistics of topological defects in graphene and related structures

TL;DR

This paper demonstrates that topological defects in certain lattice models exhibit fractional statistics, described by a doubled Chern-Simons theory, revealing new quantum properties of these defects.

Contribution

It introduces a parity and time-reversal invariant field theory describing fractional statistics of topological defects in graphene-like models.

Findings

Topological defects carry fractional charges obeying fractional statistics.

The effective theory is a doubled level-2 Chern-Simons model.

Defects are characterized by two species of semions with a new quantum number.

Abstract

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 pi/2) labeled by a new emergent quantum number that we identify as the fermion axial charge.