  The low energy sector of 2D and 3D topological insulators (TIs) exhibits
propagating edge states, which has speculated the existence of equilibrium edge
currents or edge spin currents. We demonstrate that if the low energy sector of
TIs is regularized in a straightforward manner into a square or cubic lattice,
then the current from the edge states is in fact canceled out exactly by that
from the valence bands, rendering no edge current. This result serves as a
warning that for any equilibrium property of topological insulators, the
contribution from the valence bands should not be overlooked. In these
regularized lattice model, there is a finite edge current only if the Dirac
point of the edge states is shifted away from the chemical potential, for
instance by doping, impurities, edge confining potential, surface band bending,
or gate voltage. The edge current in small quantum dots as a function of the
gate voltage is quantized, and the edge current can flow out of the gated
region up to the decay length of the edge state.
