  We study quantum point contacts in two-dimensional topological insulators by
means of quantum transport simulations for InAs/GaSb heterostructures and
HgTe/(Hg,Cd)Te quantum wells. In InAs/GaSb, the density of edge states shows an
oscillatory decay as a function of the distance to the edge. This is in
contrast to the behavior of the edge states in HgTe quantum wells, which decay
into the bulk in a simple exponential manner. The difference between the two
materials is brought about by spatial separation of electrons and holes in
InAs/GaSb, which affects the magnitudes of the parameters describing the
particle-hole asymmetry and the strength of intersubband coupling within the
Bernevig-Hughes-Zhang model. We show that the character of the wave function
decay impacts directly the dependence of the point contact conductance on the
constriction width and the Fermi energy, which can be verified experimentally
and serve to determine accurately the values of relevant parameters. In the
case of InAs/GaSb heterostructures the conductance magnitude oscillates as a
function of the constriction width following the oscillations of the edge state
penetration, whereas in HgTe/(Hg,Cd)Te quantum wells a single switching from
transmitting to reflecting contact is predicted.
