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.
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