Symmetric-Gapped Surface States of Fractional Topological Insulators*

We construct the symmetric-gapped surface states of a fractional topological insulator with electromagnetic θ-angle θ_em = π/3 and a discrete Z₃ gauge field. They are the proper generalizations of the T-pfaffian state and pfaffian/anti-semion state and feature an extended periodicity compared with their of “integer” topological band insulators counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.