The discovery of the quantum Hall (QH) effect led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two dimensional electron layer under a strong magnetic field. 1,2 The quantum anomalous Hall (QAH) effect shares a similar physical phenomenon as the QH effect, whereas its physical origin relies on the intrinsic spin-orbit coupling and ferromagnetism.

The quantum spin Hall (QSH) state is a topologically nontrivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel effect has been predicted and observed in HgTe quantum wells and in this Letter we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. The quantum well exhibits an "inverted" phase similar to HgTe/CdTe quantum wells, which is a QSH state when the Fermi level lies inside the gap. Due to the asymmetric structure of this quantum well, the effects of inversion symmetry breaking are essential. Remarkably, the topological quantum phase transition between the conventional insulating state and the quantum spin Hall state can be continuously tuned by the gate voltage, enabling quantitative investigation of this novel phase transition.

Following the recent observation of the quantum spin Hall (QSH) effect in HgTe quantum wells, an important issue is to understand the effect of impurities on transport in the QSH regime. Using linear response and renormalization group methods, we calculate the edge conductance of a QSH insulator as a function of temperature in the presence of a magnetic impurity. At high temperatures, Kondo and/or two-particle scattering give rise to a logarithmic temperature dependence. At low temperatures, for weak Coulomb interactions in the edge liquid, the conductance is restored to unitarity with unusual power laws characteristic of a "local helical liquid," while for strong interactions, transport proceeds by weak tunneling through the impurity where only half an electron charge is transferred in each tunneling event.