Symmetric-gapped surface states of fractional topological insulators

We construct the symmetric-gapped surface states of a fractional topological insulator with an electromagnetic θ angle θem=π3 and a discrete Z3 gauge field. They are the proper generalizations of the T-Pfaffian state and Pfaffian/antisemion state and feature an extended periodicity compared with their "integer" topological band insulator counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.