1 4 N ov 2 01 0 Fractional topological insulators in three dimensions

Topological insulators can be generally defined by a topological field theory with an axion angle θ of 0 or π. In this work, we introduce the concept of fractional topological insulator defined by a fractional axion angle and show that it can be consistent with time reversal (T ) invariance if ground state degeneracies are present. The fractional axion angle can be measured experimentally by the quantized fractional bulk magnetoelectric polarization P3, and a ‘halved’ fractional quantum Hall effect on the surface with Hall conductance of the form σH = p q e 2h with p, q odd. In the simplest of these states the electron behaves as a bound state of three fractionally charged ‘quarks’ coupled to a deconfined non-Abelian SU(3) ‘color’ gauge field, where the fractional charge of the quarks changes the quantization condition of P3 and allows fractional values consistent with T -invariance.