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Dirac Quantization and Fractional Magnetoelectric Effect on Interacting Topological Insulators

We use Dirac quantization of flux to study fractional charges and axion angles θin interacting topological insulators with gapless surface modes protected by time-reversal symmetry. In interacting topological insulators, there are two types of fractional axion angle due to conventional odd and nontrivial even flux quantization at the boundary. On even flux quantization in a gapped time reversal invariant system, we show that there is a halved quarter fractional quantum Hall effect on the surface with Hall conductance of p/4q e2/2h with p and q odd integers. The gapless surface modes can be characterized by a nontrivial Z2 anomaly emerged from the even flux quantization. It is suggested that the electron can be regarded as a bound state of fractionally charged quarks confined by a nonabelian color gauge field on the Dirac quantization of complex spinor fields.