  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, it has been shown
that HgTe quantum wells realize this novel effect. 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 3d 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.
