  We developed a quantum field theoretical description for the surface states
of three-dimensional topological insulators. Within the relativistic quantum
field theory formulation, we investigated the dynamics of low-lying surface
states in an applied transverse magnetic field. We argued that, by taking into
account quantum fluctuations, in three-dimensional topological insulators there
is dynamical generation of a gap by a rearrangement of the Dirac sea. By
comparing with available experimental data we found that our theoretical
results allowed a consistent and coherent description of the Landau level
spectrum of the surface low-lying excitations. Finally, we showed that the
recently detected zero-Hall plateau at the charge neutral point could be
accounted for by chiral edge states residing at the magnetic domain boundaries
between the top and bottom surfaces of the three-dimensional topological
insulator.
