Fractional Topological Insulators in Three Dimensions

Topological insulators can be generally defined by a topological field theory with an axion angle theta of 0 or pi. 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 P-3, and a halved fractional quantum Hall effect on the surface with Hall conductance of the form sigma(H) = p/q e(2)/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 P-3 and allows fractional values consistent with T invariance.