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The low energy sector of 2D and 3D topological insulators (TIs) exhibitspropagating edge states, which has speculated the existence of equilibrium edgecurrents or edge spin currents. We demonstrate that if the low energy sector ofTIs 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 thatfrom the valence bands, rendering no edge current. This result serves as awarning that for any equilibrium property of topological insulators, thecontribution from the valence bands should not be overlooked. In theseregularized lattice model, there is a finite edge current only if the Diracpoint of the edge states is shifted away from the chemical potential, forinstance by doping, impurities, edge confining potential, surface band bending,or gate voltage. The edge current in small quantum dots as a function of thegate voltage is quantized, and the edge current can flow out of the gatedregion up to the decay length of the edge state.

Absence of equilibrium edge currents in theoretical models of topological insulators