Quantum spin Hall effect

Search for topologically non-trivial states of matter has become a prime goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. We show that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes at a critical thickness. This is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. This theoretical proposal has been tested in a recent experiment carried out at University of Wuerzburg, and the distinct signatures of the QSH state have been experimentally observed. [REFERENCES: [1] Bernevig, Hughes and Zhang, Science, 314, 1757, (2006) [2] Koenig et al, Science, to be published.]