  The unconventional (half-integer) quantum Hall effect for a single species of
Dirac fermions is analyzed. We discuss possible experimental measurements of
the half-integer Hall conductance $g_{xy}$ of topological insulator surface
states and explain how to reconcile Laughlin's flux insertion argument with
half-integer $g_{xy}$. Using a vortex state representation of Landau Level
wavefunctions, we calculate current density beyond linear response, which is in
particular relevant to the topological image monopole effect. As a major
result, the field theory describing the localization physics of the quantum
Hall effect of a single species of Dirac fermions is derived. In this
connection, the issue of (absent) parity anomaly is revisited. The
renormalization group flow (RG) and the resulting phase diagram are extensively
discussed. Starting values of the RG flow are given by the semiclassical
conductivity tensor which is obtained from the Boltzmann transport theory of
the anomalous Hall effect.
