  We propose a electron-pumping mechanism called Chern pump to explain the
integer quantum Hall effect(IQHE) in the Chern insulator. By using the parallel
transport gauge in the hybrid Wannier representation we establish the bulk and
edge states correspondence in the Chern insulator. The same correspondence can
also be established in two dimensional(2D) topological insulator(TI). So we can
consider 2D TI as two time reversal(TR) related CIs put together. The quantum
spin Hall effect(QSHE) can be viewed as two TR related Chern pumps pumping
electrons to opposite directions. Compared with the Z2 spin pump, the two Chern
pumps explanation of QSHE is inherently 2D and predict that the QSHE can be
detected in isolated device, thus make the QSHE directly measurable.
