Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

Bernevig, B. Andrei
Hughes, Taylor L.
Zhang, Shou-Cheng

¹Department of Physics, Stanford University, Stanford, CA 94305, USA. ²Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA.

*To whom correspondence should be addressed. E-mail: [email protected]

Supporting Online Material: www.sciencemag.org/cgi/content/full/314/5806/1757/DC1; SOM Text; Fig. S1; Table S1; References

10 August 2006; accepted 1 November 2006

10.1126/science.1133734

Science 314(5806):p 1757-1761, December 15, 2006.

We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride-cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an "inverted" type at a critical thickness d_c. We show that this transition 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. We also discuss methods for experimental detection of the QSH effect.