Classification and analysis of two dimensional abelian fractional topological insulators

We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct the most general Chern-Simons theories that can describe these states. We then derive a criterion for when these systems have protected gapless edge modes -- that is, edge modes that cannot be gapped out without breaking time reversal or charge conservation symmetry. The systems with protected edge modes can be regarded as fractionalized analogues of topological insulators. We show that previous examples of 2D fractional topological insulators are special cases of this general construction. As part of our derivation, we define the concept of 'local Kramers degeneracy' and prove a local version of Kramers theorem.

Note:

19 pages, 2 figures, added reference, corrected typos

71.10.Pm
73.43.-f
dimension: 2
time reversal: invariance
topological insulator
Chern-Simons term
quasiparticle

References(3)

Figures(0)

[1]

The operator O commutes with Ta

[2]

For any two operators O, O′ that act on regions far from b, TaO′ v|TaOv = Ov|O′ v (F3) In other words, Ta behaves like an anti-unitary operator within the subspace of states of the form {O|v }

[3]

The state |v' can be written as |v' = Ta|v = -Sa|v (F4) The first observation follows from the fact that O commutes with Sb, and therefore also commutes with Ta = The second observation (F3) follows from TaO' v|TaOv = T SbO' v|T SbOv = SbOv|SbO' v = v|O+ S+ b SbO' v = v|(O+ O' )(S+ b Sb)|v = v|O+ O' |v * v|S+ b Sb|v = v|O+

T. Sb