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 e²/2h 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.