  We present direct experimental evidence for nonlocal transport in HgTe
quantum wells in the quantum spin Hall regime, in the absence of any external
magnetic field. The data conclusively show that the non-dissipative quantum
transport occurs through edge channels, while the contacts lead to
equilibration between the counter-propagating spin states at the edge. We show
that the experimental data agree quantitatively with the theory of the quantum
spin Hall effect.
