  We study the extra term of particle current in a 2D k-cubic Rashba spin-orbit
coupling system and the integer quantization of the Hall conductance in this
system. We provide a correct formula of charge current in this system and the
careful consideration of extra currents provides a stronger theoretical basis
for the theory of the quantum Hall effect which has not been considered before.
The non-trivial extra contribution to the particle current density and local
conductivity, which originates from the cubic dependence on the momentum
operator in the Hamiltonian, will have no effect on the integer quantization of
the Hall conductance. The extension of Noether's theorem for the 2D k-cubic
Rashba system is also addressed. The two methods reach to exactly the same
results.
