  We propose a surface-edge state theory for half quantized Hall conductance of
surface states in topological insulators. The gap opening of a single Dirac
cone for the surface states in a weak magnetic field is demonstrated. We find a
new surface state resides on the surface edges and carries chiral edge current,
resulting in a half-quantized Hall conductance in a four-terminal setup. We
also give a physical interpretation of the half quantized conductance by
showing that this state is the product of splitting of a boundary bound state
of massive Dirac fermions which carries a conductance quantum.
