  We study the role of Zeeman effect in fractional quantum Hall effect (FQHE)
on the surface of topological insulators (TIs). We show that the effective
pseudopotentials of the Coulomb interaction are reformed due to Zeeman effect,
which are quite different from those in graphene. By exactly diagonalizing the
many-body Hamiltonian in the sphere geometry, we find that the ground state
energies and the excitation gaps at $\nu$=1/3 FQHE between the $n$=$\pm1$
Landau levels (LLs) render asymmetry, and the FQHE state at the $n$=1 LL is
more robust than that at $n$=-1 LL since the excitation gap at $n$=1 LL is
larger than that at $n$=-1 LL.
