  The integer quantum Hall effect is a topological state of quantum matter in
two dimensions, and has recently been observed in three-dimensional topological
insulator thin films. Here we study the Landau levels and edge states of
surface Dirac fermions in topological insulators under strong magnetic field.
We examine the formation of the quantum plateaux of the Hall conductance and
find two different patterns, in one pattern the filling number covers all
integers while only odd integers in the other. We focus on the quantum plateau
closest to zero energy and demonstrate the breakdown of the quantum spin Hall
effect resulting from structure inversion asymmetry. The phase diagrams of the
quantum Hall states are presented as functions of magnetic field, gate voltage
and chemical potential. This work establishes an intuitive picture of the edge
states to understand the integer quantum Hall effect for Dirac electrons in
topological insulator thin films.
