Helical edge and surface states in HgTe quantum wells and bulk insulators

The quantum spin Hall (QSH) effect is the property of a new state of matter which preserves time reversal, has an energy gap in the bulk, but has topologically robust gapless states at the edge. Recently, the QSH state has been theoretically predicted and experimentally observed in HgTe quantum wells [B. A. Bernevig et al., Science 34, 1757 (2006); M. Konig et al., ibid. 318, 766 (2007)]. In this work, we start from realistic tight-binding models and demonstrate the existence of the helical edge states in HgTe quantum wells and calculate their physical properties. We also show that three-dimensional HgTe is a topological insulator under uniaxial strain and show that the surface states are described by single-component massless relativistic Dirac fermions in 2+1 dimensions. Experimental predictions are made based on the quantitative results obtained from realistic calculations.